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AOR September 2023, stuck in Language and Prohibitions, last update Sep 2024
That's the kind of blockage that probably doesn't resolve itself alone. Either IRCC is convinced you speak the language on the spot or they don't, and, well, they don't, unlike 99.9% of applicants. They either think the proof you sent is fake (lawyer up on the spot if they send you a letter saying this!), or more probably that it doesn't clarify easily that you speak the language. Did you use a foreign country diploma? If so, I'd ask for some letter from the university clearly stating the language of the curriculum and proactively send it to IRCC via webform. You know what your proof of language was and what could potentially be problematic with it, so be proactive if you can. Good luck.
Some Clarifications:
There is a big difference in whether a delay is due to unverified language ability, continuing assessment of prohibitions (which includes criminality and security background clearance involving referrals to either CBSA/NSSD or CSIS for investigation), or investigation of potential misrepresentation (such as in regards to suspicions about the proof of language submitted with the application).
For an application in process since September 2023, odds are there is a prohibitions concern and processing the application has been delayed, more or less suspended, waiting on CBSA or CSIS for clearance (a more in-depth examination if not investigation into background information, distinguishable from the formal background clearances done in batches for all applicants).
It is possible some of the delay, including continuing delay at this stage, is due to an investigation of potential misrepresentation, if there is a misrepresentation issue in the case.
BUT if that was the problem it is more likely the applicant would have already received what amounts to a PFL, a Procedural Fairness Letter. Even though PFLs often do not explicitly say they are a PFL, many times coming in the form of a request for information or additional documentation, the request is generally sufficient to alert the applicant that IRCC has concerns, suspicions about the validity of either documents or information submitted by the applicant, and the request should reference the documents or information that are in question (which, by the way, can be about information or documents submitted in previous transactions with IRCC, such as information given during a PoE examination).
An inquiry or investigation about misrepresentation could be about the documents submitted as proof of language, but if that is the situation the inquiry is not about whether the applicant has the requisite language ability. It is about whether invalid documents or false information have been submitted.
If there is any hint this is in issue, as @Seym suggested, it is time to lawyer-up pronto.
Regarding documentation as proof of language versus verification of requisite ability in an official language:
The proof of language submitted with the application, as prescribed in the instructions, satisfies application completeness requirements. If the documents submitted do not meet IRCC's requirements, the application is incomplete and will be returned to the applicant. Obviously that is not what is going on now in regards to an application made in 2023.
Otherwise, IRCC does NOT necessarily rely on that documentation for verification of the applicant's ability in an official language. If the applicant is required to participate in an interview, for example, that interview will usually (almost always) include evaluating the applicant's language ability (typically by just engaging in casual conversation to identify if there is reason to conduct a more thorough evaluation).
No matter what documentation was submitted with the application, any applicant who must meet the language ability requirement (so not old folks like me . . . in my case plenty old enough to not need to meet the knowledge or language requirements even back when I went through the process well over a decade ago) can still be screened (interviewed) to verify they meet the language requirements. Prior to Covid, when all adult applicants were interviewed, all applicants subject to the language requirement were in fact screened for language ability during their interview (no matter what proof of language was submitted with the application).
Thus, even though generally the proof of language submitted with the application is sufficient, any applicant required to meet the language requirement can still be interviewed and in that interview examined to verify they have the requisite ability in English or French . . . and any applicant who is scheduled for an interview should recognize that the interview includes screening their language ability (again, typically done through what seems like casual conversation).
If IRCC is concerned the applicant does not meet the language requirement, does not have the requisite ability in an official language, no amount of documentation from any source will suffice. So, getting a letter to bolster or clarify or verify the documentation submitted will NOT help.
Again, the documentation is about making a complete application . . . this was adopted during the Harper era to reduce the burden of processing applications for applicants who then failed language ability screening, which was very common, probably the second most common reason why applications failed prior to when CIC began requiring that proof of language be included with the application (most common reason applications failed back then, which was when there was a residency requirement rather than strict physical presence, was due to the number of denied applicants who applied relying on residency for three years prior to their being physically present for at least 1095 days, the Harper government generally challenging such applicants).
In some respects the language requirement is comparable to the physical presence requirement. To make a complete application the applicant must submit information sufficient to show they met this requirement as of the day they applied. But IRCC can, and in more than a few cases it will, conduct inquiries to verify the applicant has in fact met the physical presence requirement. Likewise for the language requirement, the applicant must submit documentation as proof of language ability to make a complete application, but IRCC can conduct an inquiry (typically an interview) to verify the applicant actually has the requisite language ability.
All that said . . . for an application in process since September 2023 it is not likely verification of language ability is holding things up. More likely something else is gumming things up. If last update was in 2024, probably time to get proactive in figuring out what the problem is.