I think this will not work. A common problem of the SIM800 module is that the power provision is not sufficient! Do not power the GPRSBee via the Stalker's 3.3V source. You should power the GPRSBee directly with an LiPo and then power the Stalker from the second plug of the GPRSBee, see
Top left red-black cable is the LiPo cable.
Try to use the SODAQ GPRSBee lib: https://github.com/SodaqMoja/GPRSbee It works for me but I did not use soft serial but hardware serial. So always have a look at your lib what TX/RX pins you are using and adjust it accordingly. On the old Stalker you had to use hardware serial (and soft serial with an additional hardware fix), the new stalker has a mini switch next to the bee socket so double check that this switch selects D0/D1 (hardware serial) or D5/D6 (soft serial) also fitting to your sketch.
I have only tested the hardware serial variant with the SODAQ lib and the Stalker 3.1!
It is also a good idea to de-activate the pin on the sim card. At least first to get it initially running.