Is what was done by the friend who sold the equipment and did not give his partner anything from its price, knowing that the partner repaired the equipment with his own money and the friend's money, considered an unlawful appropriation of a portion of his money?

If you both agree to accept these finishing works and work on them, then this is a company of bodies (partnership in labor) or acceptance of works, and it is permissible. It is permissible for the profit to be equally shared, as the profit in a company of bodies is based on what the partners agree upon, because it is earned by labor, which permits variation, and thus permits variation in profit. Rectifying defects in a partner's machine is the responsibility of its owner, and if you paid anything to repair it, you have the right to claim it. As for the price of the machine when sold, it belongs to its original owner.