Since you can send and receive with the current cable I don't see why you should change it.

Also please note that the phone might send other characters too, like more CR and LF.

You said you have only one Com on you PC, ok. You can do a "thief" with two 10K (or even 4K7) that take samples of the Tx and Rx signals while PIC and Mobile are connected together and send them to the Rx pin of the PC Com Port, just to monitor what they are doing while you are not looking. This way you will see exactly what the PIC wants the mobile to do, and what exactly is the mobile responding.

Please try to take a Screenshot of this and post it.

Ioannis