J1 transfer sponsor - please help me

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I am a teacher and I have J1 visa. I wanna change my actual sponsor with another because the first wanna change the contract and I dont agree this idea. I found another sponsor and now my point is : my actual sponsor can stop the transfer?. if the answer is Yes, can I know why? what is the condition to make a transfer?. What is "Termination at will", how can affect me this point, and if have a legal support this fragment "either party may end this agreement and visitor teacher employment hereunder, with or without cause, at any time" thank you very much for the future answer