Personally, I would welcome them with open arms, and I'll do this in the spirit of our ancestors who esteemed family...even folk who weren't even consanguineal (blood) but still considered family. Because if you turn them away, and you later find the documentation you need that proves a blood tie, they might harbor hard feelings because they were refused the first time.

But, if asked about their connection, make it clear that the family historians are in the process of verifying the exact family connection, but that you all see many strong resemblances that definitely suggest a family connection.

Is there no documentation, like the death certificate of their ancestor and your family's ancestor? Do the elderly family members remember anything about their ancestor?

Just My Thoughts...

Mel