Two questions, can you and should you?
She can be claimed as a dependent if she was a full time student under age 24, and lived "at home" more than half the year, and did not provide more than half her own support. She is considered to live at home during temporary absences including college, but not once she moves out on her own. She is a full time student if she was enrolled as the school defines "full time" for at least 1 day in 5 different months. Support she provides herself includes her income, unemployment, money from savings if spent on her own expenses, and tuition paid with loans in her name. Support you provide includes direct support for living expenses, food, clothing etc., plus a share of your housing expenses (rent, insurance, utilities) and any tuition you paid for.
There are some things you did not clearly state. If she was only a full time student in January 2020-April 2020, and did not start graduate school until 1/1/2021, then you can't claim her because she was not a full time student for parts of 5 months. (It sounds like she did not move out until 1/1/21 so she is probably deemed to have lived with you more than half the year.). But maybe she enrolled in grad school in the fall of 2020? You also need to evaluate her financial support situation.
If you can't claim her due to the full time school rule or the support rule, then that's it.
If you can claim her, she must check the box that says someone can claim her, even if you don't want to. That will disqualify her from getting the stimulus in her own name, and if she could be claimed as a dependent and skips that box to get a payment, that's tax fraud.
Then, if you can claim her, should you? As far as I know, the only time it makes sense for a parent to not claim a child who could be claimed, is for certain situations regarding the AOTC. Since her eligibility for that is over, if you can claim her, you should claim her, and possible get the lifetime learning credit at least. And she should check the box that says "I can be claimed".
