move iphone backup to a new computer

Yes, sort of, but probably not worth the trouble. Easier to just back up the phone to the new computer.

See this support link→Locate backups of your iPhone, iPad, and iPod touch - Apple Support to find where the backup is located on the old computer, then copy this entire path to the new computer, and make sure the permissions on all of the files are the same as they are on the old computer.

If the old and new computers are both Macs make a Time Machine backup of the old computer, then restore that backup to the new computer (assuming you want all of the content of the old computer on the new computer). If you only want the old backup then just restore that from Time Machine.