In the last episode of "Your Lie in April", what was enclosed in the envelope?
At the end of the episode, the photo that you mention can be seen sitting on Kousei's desk. Kaori treasured it because it was probably her only photo containing her and Kousei or even her only photo of Kousei.

It is a photo of young Kousei and Kaori plus another unnamed girl(most possible  Kaori's friend), probably after one of Karima's contests. Kaori was, most likely, there for her friend which probably participated in the said contest. There is a chance that this is the contest in which Kaori saw Arima for the first time, the one that motivated her to start pursuing music.