My mother has started doing her namaz qaza, the prayers that she missed during her youth (Alhamdulillah). She tries to do one day qaza every day and would like to do more. However, she has knee arthritis and was worndering if she can perform her other qaza prayers in a sitting position?

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May Allah increase her taufeeqat and accept her ibadaat and help her to complete the completion of the task of qadha.
If due to illness she can pray while sitting but whatever amount of the prayer she is able to pray while she is standing ask her to pray while standing.