Quick question:No one can estimate that. It's not deterministic. Test invites can be sent independent of an FP request. Several applicants on this forum received a test invite and FP request on the same day. In other cases, IRCC may wait till background check is complete, and then send out a test invite.
No one can estimate how long your background check will take, as it varies from case to case.
What do they check in background checks apart from criminal record and travel history, that it takes this long? Do they go to the applicant's original country's authorities for further checks too? If that's the case, it may be the reason for long delays in some cases.
Kindly enlighten us.
Thanks,
MW