The proby school and other training schools were located at 39/16 all the way back to the early 20th Century, perhaps beyond. The building was built for this purpose but the training requirements outgrew this site after WWII. Training facilties were later re-consolidated on Welfare (now Roosevelt) Island about 1960 centered around the old quarters of Engine 49 after it was disbanded.
The upper floors of 39/16 was the site of Manhattan/Bronx Communications office until the present facilities were built in Central Park and Bronx Park in the 1920's. The Fire College was also located there as well as the library and other FDNY administrative offices.
The old building and rear training yard were torn down about twenty years ago. Only the front facade of the building, because it is architecturally distinct, was left standing. 39/16 moved up the block for a few years during the construction. What you have is an entirely new building behind that facade. I have heard that there are commercial offices on the upper floors now.