The fact that he came across the border illegally, without a visa and crossing without being examined may prevent his application for PR.
If his documentation is false, stolen, fake or similar it may prevent his application for PR.
You need to ascertain if his documentation is genuine.
If it is, he may be able to obtain PR but I believe you are going to need some expert help in order to apply. You will have to apply "inland" if you do not want him to return to Iraq.
See:
http://www.cic.gc.ca/english/resources/manuals/ip/ip08-eng.pdf Section 5:27
5.27. Legal temporary resident status in Canada
Under the current Regulations, applicants in this spouse or common-law partner in Canada class
must have a valid temporary resident status on the date of application and on the date they
receive permanent resident status to be eligible to be members of the class.
However, under the spousal policy, applicants who lack status as defined under the public policy
(see “What is lack of status under the public policy” below) may be granted permanent residence
so long as they meet all the other requirements of the class (i.e., they are not inadmissible for
reasons other than “lack of status.”)
However, applicants who do not have temporary resident status and who cannot be granted
positive consideration under the public policy can be removed at any time. Further, the spousal
policy does not change the requirement to seek necessary authorization to visit Canada or to
work or study here.
What is “lack of status” under the public policy?
For the purposes of the current public policy, persons with a “lack of status” refers to those in the
following situations:
• persons who have overstayed a visa, visitor record, work permit, student permit or temporary
resident permit;
• persons who have worked or studied without being authorized to do so as prescribed by the
Act;
• persons who have entered Canada without a visa or other document required by the
Regulations;
• persons who have entered Canada without a valid passport or travel document (provided
valid documents are acquired by the time CIC seeks to grant permanent residence).
• persons who did not present themselves for examination when initially entering Canada but
who did so subsequently.
Lack of status” does not refer to any other inadmissibilities including, but not limited to:
• failure to obtain any required permission to enter Canada after being removed;
•
persons who have entered Canada with a fraudulent or improperly obtained passport, travel
document or visa and who have used the document for misrepresentation under IRPA. For
greater certainty, persons will be excluded from being granted permanent residence under
this public policy:
♦ if they used a fraudulent or improperly obtained passport, travel document or visa to gain
entry into Canada; and
♦ if this document was not surrendered or seized upon arrival; and
♦ if the applicant used these fraudulent or improperly obtained documents to acquire
temporary or permanent resident status.
Other cases may be refused for misrepresentation if there is clear evidence of misrepresentation
under IRPA, in accordance with the Department's guidelines.