Not quite sure I understand your question. Are you serving straight probation and looking to get into a PTD-type program in another county? Or just transferring straight probation between counties for work or living purposes?
One cannot "forum shop" for an offense as the county the DWI was in has jurisdiction over the offense.
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Unfortunately not. The DIVERT program is very specific for Harris County. In order to qualify for it you have to take a SALCE interview and then they provide you a specific program. It's essentially like deferred adjudication, but by another name. You got regular probation in Bexar and you can't swithc that into DIVERT in Harris, because Bexar has no equivalent. You can transfer your probation to Harris, but it will still be the same deal that you signed up for in Bexar. Sorry for the bad news.
No. You cannot move your cases around to try to become eligible for diversion programs. That is called court/judge shopping and is frowned upon in all 50 states.