Is the mother, who recovered the stolen machine and paid its price to the neighbors, entitled to reclaim it from the buyer who bought it for 500 pounds while knowing it was stolen, in exchange for paying him only 250 pounds?

If a person buys a stolen machine knowing it is stolen, the sale is Islamically invalid. The seller must refund the full price to the buyer, even if the buyer was mistaken in purchasing stolen goods, unless the buyer agrees to waive part of the price.

Regarding the return of the stolen machine to its original owner after compensating him: Scholars have differed on this issue:

The first view: Whoever usurps something or receives it stolen must return it to its owner whenever they are able, even if they have paid its value to the usurped party, and they can reclaim the value they paid. The second view: If the owner is compensated for the stolen item, then ownership of the stolen item transfers to the one who paid the compensation, and they are not obliged to return it to its original owner.

The final outcome: You are obliged to give the buyer the remaining price he paid for the stolen machine. As for returning the stolen machine to its first owner and reclaiming its value, this is the most exculpatory for your conscience, even if you have already paid him its value, due to the difference of opinion on this matter, and because its owner's heart may be attached to it, unless you both agree that you keep the machine and he keeps the value.