Is it permissible to leave money with a procrastinating debtor and not demand it back, hoping for compensation from Allah in this world and the Hereafter?

The basic principle is that a person has the right to demand what is due to him, and there is no blame upon him for doing so, especially if the one procrastinating is well-off. However, it is permissible to forgo demanding one's right, and there is no sin in that. If, by abandoning it, you intend to draw closer to Allah through good character and forgiveness, then you may hope for a reward, as Allah Almighty says: "And whatever good you do, Allah will know it. And Allah is Knowing of the righteous."