When you connect Gammu to phone, it does several checks on phone (I'm currently talking especially about AT based connections). Some of these checks might result in suggestions on improvements in configuration either in code or configuration. However they are a bit hidden - you need to enable debug log to actually see them.
One of those hints might allow Gammu to do much more with your phone:
HINT: Please consider adding F_OBEX to your phone capabilities in common/gsmphones.c
F_OBEX will tell Gammu, that phone can be switched to OBEX mode, which might provide access to more features than generic AT mode. The word might is important here, because for some phones OBEX does not bring anything new and using it only hides some AT functionality. This is also reason, why switch is not done automatically and you must change sources to do this. I'd gladly accept patches, if you have successfully tested F_OBEX with your phone!