I do not understand the question. And I am NO expert.
Generally a traveler (Canadian citizens and PRs included as well as FNs) must TRUTHFULLY answer questions posed by CBSA officers during a PoE examination. Deliberately untrue statements, or omissions to deliberately conceal information, are of course misrepresentation. The import and impact can, however, vary widely depending on what and why and how the information is material.
No need to volunteer information to CBSA at PoE:
Generally, a Canadian traveler ONLY needs to truthfully answer questions at the PoE and does NOT need to otherwise volunteer information. In particular, other than obligations to affirmatively make certain CUSTOMS related declarations at a PoE (such as declaring weapons or possession of more than $10k in currency, including gold and such), a traveler generally only needs to answer questions asked . . . no obligation to volunteer information (again, except as to certain mandatory Customs related declarations). BUT if a question is asked, the traveler MUST answer truthfully (or, if a PR or a citizen, the traveler could decline to answer questions beyond the scope of identity, status, and Customs related matters, but of course that tends to escalate suspicions, resulting in further inquiry, and can have some negative consequences).
Thus, if asked, the PR is required to answer truthfully. If not asked, no requirement to volunteer information such as the PR has criminal offence charges.
Affirmative Obligation to Declare Arrest, Pending Charges, or Conviction for Criminal Offences:
If asked a question about criminal offences by any lawful authority, a person is required to answer truthfully. I believe giving false information to a law enforcement or other officer (CRA, IRCC, CBSA, among others) is itself a criminal offence. For Canadian citizens as much as anyone and everyone else.
Whether or not, or to what extent, giving false information of this sort constitutes a "misrepresentation" with immigration status consequences, depends on many particular factors including of course the context. (Is it during a PoE examination? in an application of some sort? an interview with IRCC? a casual conversation with a CBSA officer you happened to meet in a bar?) In general terms, any material misrepresentation made to obtain status in Canada, or entry into Canada, constitutes misrepresentation under IRPA, and can be grounds for determining the individual is inadmissible to Canada. Whether a FN (Foreign National) or a PR. (Only Canadian citizens have a Charter right of entry into Canada and thus cannot be determined to be inadmissible.)
Affirmative obligation of certain APPLICANTS to inform IRCC of criminal offences:
Unless asked (such as in an application), I am NOT aware of any general obligation for a PR to notify IRCC of criminal offences. However, there MAY be such an obligation in certain circumstances, such as if the PR has an application pending for which the PR was required to disclose, in the application, information as to any such information.
In this regard, MOST IRCC applications require the applicant to NOTIFY IRCC of any material changes in the information provided. Thus, if the application requires the disclosure of criminal offences, the applicant is required to NOTIFY IRCC if after applying the applicant is arrested, charged, or otherwise has a criminal matter. Failure to do so is a blatant misrepresentation.
For example, as I recall (without revisiting the procedure and forms), a PR sponsoring a spouse for PR must declare whether the PR has had any domestic violence related offences. And the obligation to disclose any such offences continues while the application is pending.
Citizenship applicants must specifically declare information related to criminal offences. If an arrest or charge arises after the application is made, it is the applicant's obligation to promptly inform IRCC of this. Failure to do so is misrepresentation. (Note: for citizenship applicants, the obligation extends to offences charged anywhere in the world, in any country not just Canada.)
I am not aware that the application for a new PR card asks for information about offences other than asking whether the PR has been subject to any Removal Order. So, if a PR with a PR card application in process is charged with a criminal offence while that application is pending, I am not aware of any obligation to notify IRCC of this.
Observations about sharing information between CBSA and IRCC:
Both agencies have access to GCMS, the Global Case Management System. While this system was predominantly organized to facilitate integrated records for use in processing particular applications, it appears to be a centralized, comprehensive repository of information about individual clients apart from (in addition to) any specific application in process. Access to this information is, obviously, restricted. My sense is that access depends on who is seeking access, what information in particular they are querying, and why. My further sense is that CBSA and IRCC officers have general access to basic client information: identity, vital statistics (DoB for example), status, last known address, and probably any alerts. Not that they have authority to check this information out of personal curiosity, but they can access this information with little more than a notation in the GCMS that they have accessed it. Thus, for example, a CBSA officer at a PoE can query the system without having to document any particular reason for doing so.
Included in or related to GCMS are
-- FOSS (Field Operations Support System)
-- CAIPS (Computer Assisted Immigration Processing System)
-- QRC (Query Response Centre)
Much about what information is open to both IRCC and CBSA in these is confidential, not revealed to the public. BUT suffice it to say, there is a lot of information in these systems readily accessed by either CBSA or IRCC.
For example: While I am not privy to just how it works, in general terms information in FOSS can include criminal record queries . . . so either a CBSA officer, or an IRCC officer accessing the client's GCMS, can readily see if the client has criminal history hits in . . . I am not sure which databases specifically, but at the least the equivalent of name-record hits in either the RCMP databases or the U.S. NCIC/FBI databases. Thus, for example, allowing for continuing flaws (holes, or incomplete information), when a CBSA officer accesses the client's information, or when an IRCC officer queries the client's GCMS, it should ordinarily reveal any criminal history hits, including (I believe) recent arrests or charges in either the U.S. or Canada (I'd guess INTERPOL as well, but I am less confident of this).
General Observation About Criminal Offences and Immigration Status or Proceedings:
On almost all fronts, but as to immigration and criminal records in particular, government record management functionality continues to expand and improve, largely facilitated by continuing enhancement in technology but also by expanding policies and practices as to capturing and storing data, and facilitating access. The integrity and accessibility of records in regards to criminal matters, in particular, is especially reliable and approaching completeness.
My sense is that going forward, misrepresentation related to a failure to disclose criminal matters will be the most common type of misrepresentation IRCC and CBSA catch and prosecute, and it is already the easiest for the government to prosecute (given the nature and integrity of criminal records). A PR with a citizenship application in process who is arrested while the application is in process would be utterly stupid to remain quiet about it and hope IRCC does not discover it . . . this is perhaps the main type of misrepresentation IRCC is likely to discover sooner or later, and even if much later it is perhaps one of the most likely to lead to revocation of citizenship.
As multiple official cases have shown lately, even if the charges are later shown to have been totally unfounded, the failure to disclose them is a misrepresentation, the record of the court proceedings is virtually enough to make the case, actual innocence is NO defense, and the consequences are severe.
