I do not know. It seems to be dangerous if you changed your situation and you did not tell them...
I suggest you to tell them as soon as possible and explain to them very clearly
1. you are phd students, give them your phd contract and let them know you are 3-years CDD.
2. you can also give them the document that proofs you are phd students, which you can get from the graduate school you registered
3. your salary bill you get every month (it depends, if you go to CAF, then take it, if you mail the documents, you wait until they ask for it)
4. all the documents that proof your identity (Passport, Visa or Titre de sejour (scientific)....)
All the people I know who also change from student to scientific, they all keep getting help from CAF. You do not need to worried about that. If they refuse to give you help. You go there directly and I think you will get the correct help!
If now you are getting something you do not supposed to get.... It is good to return it back before they find it out... It is my way of doing things...
Anyway, you can do what you want. You are doing phd so you must be able to decide this. I just tell you my experience and hope it helps!
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