Living in 2 states, 1 temporarily

I am doing my elderly mother's 2020 taxes for her.  She has lived in Pennsylvania for many years.  In June 2020, she moved to live with my sister in Delaware.  After 3 months (in early September), she decided to move back to Pennsylvania.  Her income consists of pension, social security, and some investments.

 

Do I need to file part-year returns in both Delaware (3 months) and Pennsylvania (9 months)?

 

Thanks.