Is it possible that to find a particular login belongs to which group?

I can see a login created with windows authentication in server A. I am not sure is it included in any group or not in serverA.

Server A has linked server with B.

But I didn't see the same login exists on server B.

so how to find that the login belongs to a group or not in B and as A?

Here serverA means Sql server, is installed on machine A and Sql server B is installed on machine B.

It is able to select the data from the linked server but not able to update. They are saying it has update statement will also works?