[robrain]

Messages, select user, click the user icon to get to the info page, click Photos, Edit, Select, Download -> photos are in the Photos app and you can do what you want with them.

Not the easiest operation, but hardly jealously prevented.

[robrain]

Self-reply addendum - individual photos can be dealt with with a simple long-press, no need for delving into the info page for the user.

[rhyperior]

And do that individually for each of the thousands of photos? There’s no select All. Yikes.

[m463]

yes, photos/camera roll is ok... if you mount an iphone as a usb device you get the DCIM/IMG_0000.jpg kind of thing.

But text messages are jealously guarded and not exportable. Apple does this for itself, not its users.