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I'm not quite sure if I understand correctly your question, but I can think of 2 options to accomplish this:
1. Cloning: This method allows the other user to create a copy of your form and keep it on his/her account. However, if a change is made in any of the forms it won't be replicated to the other one.
2. Sub-User: You can add the other user as a sub-user in your account and this would grant access to your form so he/she can make changes to it.
Hope this helps.
Let us know if you have further questions.