ZMA Controller described a airspace incursion event when an aircraft in hand off status appeared to have been accepted by PBI Approach but had in fact not been accepted and/or handed off via automation.

Narrative

A PAY4 was a SUA arrival routed STOOP then SUA. The airplane was instructed to cross STOOP at 4;000; and an automated hand off was initiated to PBI Approach. The airplane was instructed to contact PBI Approach after the hand off appeared to be accepted. While myself; the D-Side Trainee; and Trainer discussed the operations taking place at two other airports not relevant to this event; the Controller at PBI Approach contacted us via land line to inform us that he did not show the PAY4 being handed off to him. At this point; the data block reflected to be under my control once again; and had to be redirected to the specific sector in PBI Approach. At this point; the airplane was already inside their area of jurisdiction. Whether the track control of the data block changed from PBI Approach to the Center without any inputs; or whether it changed due to an input from myself or the D-Side is unknown. Recommendation: always remain vigilant of all airplanes in your sector; even to those no longer in radio contact. Additionally; refrain from making changes to a data block after a hand off has been initiated (maybe a change of interim or assigned altitude caused the event).