For me, I did the two targets SA/SO and then decided to see if I could get to the cable car exit via suit only. Once I realized that the recon gear is hostile inside the clinic as well, I aimed to get to a patient outfit (which I did - through the kitchen, up the stairs, into the central bathroom, and lure a patient to KO and take his patient outfit.
I then went to Portman’s room and the letter was there.
It may just be that it takes time to appear? Or that you have to get there without being spotted?