It may be possible, you will need to speak to the community supervisor and California has to agree to accept the transfer. It is best to do all this before entering into a community supervision arrangement. Other alternatives may include reporting by mail or early termination if you have successfully completed all the requirements of the community supervision.
You need to tell your probation officer you want to move to California, and specifically where. He/she will have to contact California to see if that county will accept you as a probationer. There is no right to a transfer out-of-state. In no circumstance do you move without approval from your probation officer. Unknown as to how long the process will take.
First, you cannot transfer the charges at all. They are in Texas and there they will remain.
If you get probation then even the you may or may not be able to move to California - it is up to California whether or not they accept you UNLESS you were a resident of California at the time of the offense and then they must accept you.
You need to hire a Texas lawyer.