Does the mother deserve the original deposited amount (55,0 EGP) without the increase resulting from the rise in the price of gold, and does the son deserve the increase, or should it be divided?

Appropriating someone else's property without their permission is considered usurpation (ghasb) which necessitates compensation if the property is damaged or diminished. As for its profits, there is a difference of opinion:

- The Shafi'is and Malikis: The profit belongs to the usurper, as it is a result of their effort, and they are liable for the property (al-kharaj bi al-dhaman - benefit follows liability).

- The Hanafis and Hanbalis: The profit belongs to the owner of the property, and the usurper is not entitled to any of it.

- Sheikh al-Islam Ibn Taymiyyah: The profit is to be divided between them, because it resulted from the owner's property and the usurper's effort, similar to a Mudarabah partnership.

Therefore, the questioner's mother should take the principal amount and half of the profit, after deducting what the questioner previously paid her.