Yes, it does matter.
You say he met all the requirements to be your dependent.
Then he can not meet the requirements to not be your dependent.
Key among these is the Support test and Residency test under Qualifying child.
If he was not independent until September, and you provided his support the other 8 months of the year, he fails on providing over half of his support,
If he meet the residency test when you say he met all the requirements, then he cannot have lived somewhere else for over six months.
Only one can satisfy the eligibility to claim a dependent. It is not a commodity that can be moved around.
If he met all 6 requirements to be considered your dependent this year and you chose, for whatever reason not to claim him, he still cannot claim himself.
You still would be the only person eligible to claim him - you are the only one meeting the 6 tests.
IRS Fact Sheet - Qualifying Child
