All that is known to me about @Hans Boysen comes from Melchior Krafft's _Zweihundertjähriches Jubelgedachtnis_ (1730): "Der zweyte [Sohn von Petrus Boethius oder Boysen], Hans, ein Bürger hieselbst, so ohne Kinder gestorben". It is my informed guesswork that this brief reference by Krafft to the supposed childless death of Hans was based on the absence of information of descendants of Hans.
There seems to be no trace of Hans Boysen beyond the above-mentioned birth lineage at all in the reported family life. I could not find any record of him in the region from whence he came. It appears to me that there is a high possibility that he may have left the region as a youngster upon entering adulthood.
It is my well-considered opinion that Hans Boysen may have been the @Boy Boijesz who arrived at the Cape of Good Hope on 24 September 1686 and who became the founding father of the Boysen (today: Booysen) family line in South Africa.
Any information on the life of this person would be a great help to try to establish whether my hypothesis on a connection between Hans Boysen and Boy Boijeszoon holds water.