Hello Pjl54 and welcome to Apple Support Communities.
I see you have a question about how to save pictures that were sent via the Messages app. That process has changed a little but under iOS 13.
- Open the message.
- Tap the name of the contact at the top of the message, then tap .
- You'll see Images and Attachments. Touch and hold an image or attachment to show options like Copy, Delete, and More.
To save an image or attachment outside of Messages, tap an image or attachment, tap , then select an option like Save Image or Save to Files. When you tap Save Image, it saves it to your Photos app."
Use Messages on your iPhone, iPad, or iPod touch
Cheers.