Any Recommendations for a dead Logic Board?

My moms laptop seems to have gone caputs. A repair guy she went to says it seems to be the Logic Board and she'll need to replace it. The problem is that she's adamant about keeping the files that are onboard.

She doesn't have access to the iCloud account on it because she can't remember which one it is...

So I'm thinking the only other option is to have a Micro Solder Specialist take the SSD's attached to the broken Logic Board and solder them to the new one.

I'm no specialist, but I think this sort of work would require someone with a huge amount of experience in this sort of work.

Does anyone have any recommendations for specialists online we can ship to for the work?