Married Filing Jointly??? Please HELP

My son is a US citizen and he has married a UK resident 3 years ago.  They have been attending graduate schools in US and UK respectively so my son has been filing his tax return using "married filing separately" status.

 

My daughter-in-law visited my son in February 2020. Because of the COVID, she has been stuck in US. As a result, she has decided to apply for the change of status (permanent resident - Green Card) last May. Paperwork has been moving very slowly yet steadily and she is now waiting for the interview to be scheduled.

 

The question is: for year 2020 tax, can my son file "married filing jointly" since they have been living in US for almost the entire 2020? However, she has not received her Social Security Number yet. If using married filing jointly status, how can she enter the SSN? 

 

Thanks