Do you have SSH/root access on both servers ?
It will be better keep PHP version same on both servers, so we can just do the migration and don't have to deal with problem with changing PHP version. If you have cpanel and SSH root access we can do that. Changing PHP version can cuase problem if he script do not support newer PHP version.
I have 16 years of experience in web hosting, server administration and php programming
See my previous works at
https://www.freelancer.com/u/NetFreeHost
Message me, let's discuss the project.