Quick solution
devel-su
vi /usr/share/applications/jolla-messages.desktop
at the end of line Permissions=Contacts;Messages;CommunicationHistory;Privileged;Ambience;Sharing;RemovableMedia add ;Pictures
it should looks like this Permissions=Contacts;Messages;CommunicationHistory;Privileged;Ambience;Sharing;RemovableMedia;Pictures
Save file
After relaunch Messages app it will be possible to save images from MMS