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YOu woud need to visit a local computer repair shop, that is APPLE certified for the hard drive swap you are wanting to be done.
On an Mac the back and restore function is done in the cloud.
So, i suggest you do the BACKUP yourself, as SOME shops do NOT do this service, as it requires login credentials to be able to do it properly.
But some shops DO offer this feature, the shops that DO will be APPLE certified.
I suggest you take the computer to an APPLE certified repair shop.
They WILL be able to do the backup.
So, yes, an Apple certified Repair shop WILL be able to do the BACKUP, then hard drive replacement, and then a RESTORE.
They may charge extra for this service, but they can do it.
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