What should I tell schools when my supervisor sent me a recommendation letter and said she has no time to upload it? I'm applying for Ph.D. programs so I requested a recommendation letter from one of my supervisors in my master's program. She directly sent me a strong recommendation letter in the email but said she has no time to upload it online. 

The thing is her daughter just had a premi baby and she needs to take care of them. I worked closely with her and she is well-known in my field. Her recommendation letter will be really helpful. What should I tell the schools I'm applying for? How should I explain my situation?
Tell the school(s) exactly that (leaving out the baby and so on) and ask for advice. They may make some exception (or not). Maybe permitting you to submit. Maybe being lenient on deadlines. Maybe contacting the professor themselves (if you provide her email.) 

You could also ask her to send the original email directly to them, rather than dealing with the online system. 

Apologize for the inconvenience, even though it wasn't you that caused it. Just a polite ritual. 



Dear x

I apologize for the inconvenience, but my professor sent me the enclosed recommendation but was unable to find time to upload it due to a family emergency. She can be contacted at y@z.edu for verification if needed. 

If this is not acceptable, please advise me on ...

Sincerely X Z