Is it permissible to demand the application of an installment purchase offer after agreeing to a cash sale and paying a portion of the amount, especially since I have not formally relinquished the shop and the buyer's financial circumstances have not changed?

It is not permissible, according to Islamic law, for a seller to demand from the buyer more than the agreed-upon debt in exchange for a delay in payment; this constitutes usury (riba). The sale has been concluded, ownership of the commodity has transferred to the buyer, and the seller is entitled to the full agreed-upon price. If the buyer faces financial hardship or procrastinates, the seller is not permitted to increase the debt. The seller is only entitled to demand the agreed-upon price from the buyer, to sue him, and to mortgage the sold item until the full price is paid.