ATC Watcher...
Yes, I agree with your points re responsibility for control near FIR boundaries. You got me thinking also about the greater number of incidents that occur near FIR boundaries; for example, occasions when flight plan info wasn't passed, or coordination wasn't completed. In those scenarios, as you know, there is a greater risk of an incident near a boundary.
One curious statement (among many in this case...) was the statement by the Senegalese that they watched the HS-125 until it disappeared from radar at a position about 56 nautical miles west of Dakar (by the Lat and Long given) and that they were surmising the loss of transponder return at that point was due to fuel exhaustion. For an IFR aircraft to run out of fuel about 8 minutes past its destination makes no sense (IFR fuel reserves etc). In this case the flight planned alternate was Bamako, Mali, which makes the “fuel exhaustion” statement even more suspect.
There is of course the possibility that damage to the HS-125 included some kind of fuel tank or fuel line rupture, which could in turn lead to a much reduced range. But that proposition raises other questions that greatly reduce the probability of that scenario (even without considering the famous Mr. Occam…).
The statement by the Senegalese re the transponder of the HS-125 seems to negate the idea that a lack of operating transponder on the HS-125 would have been a factor in the mid-air collision. Whether the B-737 had an operating transponder, we don’t yet know. (We cannot assume an operating transponder, even for a relatively new aircraft, especially in this part of the world.) If both aircraft had operating transponders (on and functional) then why no TCAS alert? Or, if TCAS alert, why no avoidance manoeuver? There is obviously the separate, but related, issue of why no separation between the aircraft? Was separation not being applied, or was separation lost, or? Time will tell…