I am so glad you asked.
If Edward Elmer is in your personal family tree, now is the time to go there and clean it up. Make sure he has an Unknown father, mother, brother and sisters if you had previously entered them. Check your sources and correct them where they have erroneously added these family members.You should not remove the sources, rather add a note where appropriate to correct them. Anderson's TGMB was proved accurate.
Personally, I believe Edward Elmer-195 and Theophilus Aylmer-35's son Edward (soon to be entered) are the most likely candidates to be one and the same. As others have said, there is not proof that such is the case, yet.
As our analysis concludes, DNA will most likely be the defining fact to prove family relationships on this and other families. There are more people joining their DNA results with ours and eventually, we should have conclusive answers.
Additionally, Elmer-195 should be PPP Protected at this time.
Unfortunately, the essay was too long to fit in G2G and so the best I could do was a link. Any suggestions?