Can I apply for a stimulus check for my deceased mother

No, you cannot. A deceased person is not eligible for a stimulus payment.

If your mother died in 2020 and you (or her personal representative) are required to file a 2020 tax return for any 2020 income from before she died, that might include a stimulus payment.

The IRS has ruled that deceased persons are not eligible, but the legal basis for this and the timing are unclear to me.  For example, the CARES act was passed on March 27, my mother passed away on April 7.  What is the legal basis for saying she does not qualify?  I've never seen that explained.  Suppose the payment to my parents had been made electronically on April 6 instead of May 6, what is the legal distinction in the CARES act (separate from the IRS interpretation of the CARES act).

In any case, you can't "apply" now.  We don't really know what will happen on the 2020 tax return.