Thank you for letting us all know. I just want to add this. One of the births I looked at earlier today was
Thomas Rogers reg Mar Q 1912 @ Bucklow ( which is on the border between Lancashire & Cheshire) mother's maiden name Rogers. Which would probably mean that she was a single mother at that time The GRO ref. if your friend wanted to order the cert is Volume 8a Page 382
Sale is one of the districts that was covered by Bucklow in 1912. It's just possible that Thomas was actually born Dec 1911 and reg in the 1st Q of 1912 . But without buying the cert and checking it

And David's suggestion re DNA testing is also a good one
Good luck with your search
Lemur41