What kind of phone is it?
What do you mean "updated" ?
There is no easy way, if there is a way at all.
If there are backups that were made during that time, those messages would be in the backup. If you restored from that backup, the messages would be on the phone.
What I am saying is that if you have a backup in iTunes that was made when the messages were on the phone, if you restore that backup to another phone, you may be able to see those messages.
Transferring contacts, etc is not the same as transferring messages. So if you did not specifically transfer messages, they would not be on the the phone.. and even if you did, and they were deleted over a year ago, chances are low that they are recoverable.
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