I only have the basicest of basic mobile phone as I hate phones.
I do get sent messages from family though and have kept them back to when my granny died. I haven't saved them as I didn't know how. Some are horrible but they are evidence and history.
When my little brick mobile phone packed up I put the sim in the new phone. That was years ago.
Today my phone said sim error and they are all gone.
I should have written the messages down on a piece of paper shouldn't I.
Afraid so. It's a bit late for me to mention it now, but I think you can have a sim card reader on a PC (probably USB) for copying stuff over.