I just got my Mother -in-law a Lumia 435 on T-Mobile. When I sent her a picture via text it showed up from mobile operator- media content in this message. But when you tap it says no longer available. Anybody see this before?
Is the phone running wp8.1 or win 10 mobile? If its running win 10 mobile, look up the proper apn settings and apply those. If its running 8.1 you can either apply the apn settings or bring it into a T-Mobile shop as that's the official os that T-Mobile will support for that phone.
Does your mother have data on her plan or just minutes and text messages? If she doesn't have data, that's why she can't see it. Picture messages are not actually SMS, but MMS.
As BluWarrior said, check the APN. T-Mobile phones shouldn't require additional setup with the APN because it is detected when you put in the sim.
She has data and it's on 8.1 denim. She took it to T-mobile and they couldn't figure it out. It's one of the primary reasons she wanted the phone. So she can get pics of the grand kids. I am going to call customer support this weekend and see if they can figure it out.