I've been playing around with the A6 Gprs chip from Ai thinker.
So I was able to send a SMS:
AT+CMGF=1
AT+CMGS=0031612345678
Is it (technical) possible to change (spoof) the sender phone number? Or can I do it with other chips, like SIM900?
Typically the phone number is not stored in the SIM card. You have IMSI inside the SIM card and this IMSI binded with your phone number and an authentication key named Ki in the network operator's databases.
When you want to use the operator services, your device (The chip, the handset, etc) send the SIM Card's IMSI to the network operator. Network operator search his database for that IMSI to see if that IMSI is valid or not. If it found that IMSI inside the database, then it generate a random number and encrypt it with the corresponding Ki (that is stored in the database) and returns that encrypted data to your SIM Card. As your SIM card is aware of its Ki, it can decrypt the random number and return it.
Finally if the network operator receive the correct random from the SIM card, your are authenticated to the network. after that, when you call someone or send a message, the network operator concatenate the phone number inside the database with your messages and send them to the other side.
So, no you can't!