Is this furniture considered an inheritance for my mother and sister, or does it belong to the questioner?

The ruling varies depending on the intention of the questioner and what he did when furnishing the house. If he gave the furniture to his mother as a gift and transfer of ownership, then it belongs to her and her heirs. However, if it was given as a loan (عارية) or permission to use (إباحة المنفعة) without transferring ownership, then it belongs to him and does not enter into her inheritance. The difference between transferring ownership (تمليك) and granting permission to use (إباحة) is that transferring ownership implies the right to dispose of the item, whereas granting permission removes the impediment to consuming or using something that is not owned. A gift (هبة) is a transfer of ownership without compensation, and the ownership of the giver ceases. As for granting permission to use, the ownership of the grantor does not cease, and the one granted permission is not allowed to dispose of it in any way other than what was permitted to him.