I tried to modify my hardware setup to detect whats going IN and OUT in the GSM module (below). I test each button(Button1-Button3) and each corresponding response of the GSM shown in the serial communicator.
Name:  pic_gsm_pc_view.png
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I noticed that everything seems normal..but when I tried the connection PIC-GSM... I have the same issue.
So sending PIC to GSM AT commands is not issue..I think when receiving incoming data from GSM to PIC is where the trouble is.

Regards,
tacbanon