Is it permissible or forbidden to divide profits between two partners and leave one-third for the company, and is the partner's mother entitled to a percentage of the profits in exchange for the amount she lent to the company, which has been fully repaid?

The profits are divided between the two partners according to their agreement. If there is no agreement, then the contract necessitates equal sharing of profits if the partners are equal in work and capital. As for the lender to the company, he is not entitled to a share of its profits, and it is not permissible to stipulate this, because it is usury (riba). However, if the two partners willingly offer an increase when repaying the debt, there is no objection.