Q: how can I back up my text messages showing the date and time received?

by using google search for program that can do that, I suppose.

This here is iCloud on iOS forum, iCloud backs up your texts inside of your phone backup and puts it back on other phone, but sometimes those

backups become corrupted and then other program can be used.

May be someone who knows the name of program like that can chime in, but I would not really rely on such submission, without my own research.