Is the lifetime learning credit apply to us (just become residential alien from non-residential alinen)

My spouse and I were Non-residential aliens before 2020.  2020 Tax year is the first time I become a residential alien, but my spouse is still Non-residential aliens. I know when we file jointly, he should be considered as a residential alien. 

 

My spouse started graduate school A in 2019 fall and paid the tuition out of his pocket. He finished it and started graduate school B in 2020 fall and got funding as a research assistant.  

 

As he is a non-residential alien, neither school gives him form 1098-T. However, it seems for school A, he can claim credit ( when he files with me, he is residential alien. and he paid school A out of his pocket). 

 

1. Am I correct? Should he ask for 1098-T from school A? 

2. I tried this credit section in turbotax (assume he will get the 1098-t) and turbotax asked " did xx ever receive the american opportunity or hope credit', I answered no (we never got it as we were non-residential aliens). And turbotax concludes that he will get 'lifetime learning credit' for  $2000. Is this correct?