I have two "Mystery Cousins"

On another service my number one match is at a THIRD cousin level to someone who on a paper trail tree is actually a fifth or sixth degree cousin. His daughter shows up as a very distant cousin.

I imagine there must be someone closer that's not on his paper trail tree which isn't as detailed as mine.

This "other service" is not very transparent - not showing details like shown here or in the off again on again GEDMatch.
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The other mystery cousin has a major brick wall in one branch of her family and I also match her cousins from the brick wall branch of her family. She and I are at about 4th/5th cousin level.

If these two mystery cousins had their DNA data transfered here would FTDNA be able to help us figure out our respective common ancestors?

Thanks!