I finally reached the point where one of my characters has purchased all 195 specialization skills, but I keep earning specialization points. (I had several banked that I spent to reach this point, leaving two surplus. I have since earned two more.)
Specialization points in excess of the 195 needed are supposed to auto-convert to dilithium. Mine have not. Nor are they transferrable to another character on my account (which would be nice, but is not how they are designed to work... just a suggestion.)
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From the Wiki:https://sto.gamepedia.com/Captain_Specialization
Note that bonus Specialization points, such as from Featured TFO Rewards or Admiralty (Federation Tour of Duty 10 namely), earned prior to Season 11.5 do not count towards this limit. Points earned prior to this will simply add to your total limit before conversion starts.