Stimulus checks eligibility as filing tax return as married-separately to my foreign spouse.

I'm a U.S. citizen, I live with my foreign wife overseas.

 

My question, I understand that my wife is not eligible to receive any stimulus check as she does not have an SSN, am I eligible to receive the stimulus payments? taking into consideration that we have filed our 2019 taxes as married-jointly, also, would it help if we are going to file our 2020 taxes as a married-separately?

 

Please note that I have received the first stimulus check already as it was based on my 2018 taxes when I was not married then. Therefore, I'm not sure if I'm eligible to receive the second the third payments.