Can I transfer pictures from 1 iPhone to another

If you have the Apple ID and password, or have legacy access (see below), yes.

I’d start with getting backups of everything, as mistakes can happen.

It’s basically the same as an Apple ID migration, merging of some or all of what can be transferred to a second Apple ID.

Here are some previous discussions of that:

Apple ID - Apple Community

Stop sharing Apple ID with wife - Apple Community

If it’s solely the photos and you have or can rent enough iCloud storage for the transfer, you can also transfer the photos through iCloud and Family Sharing and the shared photo albums, possibly creating one or more shared albums as needed. This can be combined with sorting the photos.

AirDrop also works, but that can get tedious with lots of photos.

If you have a Mac or Windows computer: Download iCloud photos and videos - Apple Support

If the originals are stored on iCloud and you use another photo-sharing service: Transfer a copy of your iCloud Photos collection to another service - Apple Support

And for everyone (else) reading here:

… How to add a Legacy Contact for your Apple ID - Apple Support (add this for yourself)

… How to request access to a deceased family member's Apple account - Apple Support

Sorry about the loss of your mother.

These are the steps you should perform (if you do not know her Apple ID & Password and/or her passcode to unlock that device):--> How to request access to a deceased family member's Apple account - Apple Support

Then follow the suggestions provided by MrHoffman.

Regards

Giulio