Time machine backup not fully restored

Dear all,

I would like to migrate from an MacAir to an MacBook. I have regularly backed up to a NAS storage using time machine.

When migrating to the new Mac, I am able to use the NAS time machine backup for migration and the new Mac starts up alright. However, I noticed that a few things are not restored: Most importantly, Mac Mail is not restored. For one user, no emails are shown. The accounts show up, but no connection possible. For another user, the Mac Mail starts up, just a a fresh installation.

Both Macs use OS X 10.12.6.

Please advise how to ensure that the backup includes ALL files on the old Mac (no folders are excluded in the list).

The same procedure has worked perfectly with another Mac and a hard drive for time machine recently.

Thank you!

The_chemist