Happy Friday, magenta3701707!
Welcome to our Support Community! As Mike mentioned above, a data connection is needed for group SMS and MMS. I'm just as curious as he is - did you have WiFi connected when you downloaded the messages previously? We don't have any troubleshooting to complete if the messages are able to be downloaded once you have mobile data enabled.
Hey there, magenta3701707! Just wanted to check in here again and see how things are going. If you're still having trouble with this, please take a look at the questions that Mike & Amanda asked and let us know a bit more about what's happening! Thank you!