The shoulders are incredibly complex, so when addressing one deficit, like a lack of overhead reach, you have to realize there are multiple things to address throughout the interconnected tissues.
For instance, if your shoulders are tight, you cannot even begin to work on them without first loosening the chest, biceps, and lats.
As mentioned above, desk-sitting exacerbates the issue for many adults. It shortens the pectorals and rolls the shoulders forward. So while weightlifters need the following, it's doubly true of desk sitters.
Start by stretching out your chest and pectoral muscles.