Inhyseshj. is an abbreviation for inhyseshjon.
A person who had a (shared) bed in someone else's house, typically free of formal rent, just helping out. Sometimes an inhyseshjon had his/her own household (own store of food etc.), sometimes not.
An inhyseshjon most often made a tiny living from some sort of cottage industry and/or from temporary jobs as an extra hand during harvest etc.
In Norrland an inhyseshjon meant a person who had a tiny cottage or mud hut on someone else's land, free of charge or just paying a nominal rent by doing odd jobs or sharing the results of hunting or fishing.
In some cases an old crofter who had no children would allow a young couple to take over the croft very cheaply or even for free if he was allowed to stay on as inhyseshjon - in this case it was full board, and the original crofter may even have been allowed a separate room.
A hjon basically means person; today the meaning is often associated with words like fattighjon (poor person, so destitute they received support from the parish), but the original meaning is a member of the household.
Ingela