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which is the correct one, "her and her partner's research proposal was accepted," or "She and her partner's research proposal was accepted?"

i'd appreciate your help!
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The former.

Or, to be more precise, both of them, but they mean different things. "Her and her partner's research proposal was accepted" means "The proposal which was jointly created by (1) her, and (2) her partner, was accepted". Wheras "She and her partner's research proposal was accepted" means "(1) She herself was accepted, and (2) her partner's proposal was accepted".

(Strictly speaking, "She and her partner's research proposal was accepted" is an error in all circumstances. It could only be interpretted in the way I described above only if "was" were replaced by "were". However, it is possible that someone listening to this sentence may miss that distinction).

I assume you meant the former, so it should be "Her".

Rommie