Hey there! We'd need a lot more information before we could provide any advice.
The first thing to check would be the transfer log, which you can find in the WHM >> Review Transfers and Restores area. If there was an issue with the packaging of the data on the Source machine, I would expect it to show up there. If the issue was on the restoration side of things, that would also show up.
If there is no issue shown there, I would try manually packaging the account on the Source machine (/scripts/pkgacct username) and then manually extracting the files on the source to see if the emails are in place.
One of those things should at least provide a clue as to where the issue lies.
