File server from domain A to B. Don’t want to loose user file permissions!

I have a file server which is currently located in Domain A. I want to migrate this file server to Domain B. The actual migration is not the problem; the problem is how I can make all the user permissions to migrate to the new domain?
To give some more detail, the majority of the users have access to various files and folders within the specific file server, all the distribution groups are located in Domain Controller A and I want when I do the migration all these permission to be transferred across to the new domain, which has Domain Controller B.

Is that possible? I have never migrated a file server before.

Thanks in advance