Is the dry ablution (tayammum) and the first prayer of a person who has experienced a wet dream valid if he performed tayammum with a smooth stone due to lack of time, and is there sin incurred by delaying the re-offering of the prayer after knowing the correct ruling?

The ruling on performing tayammum with a smooth stone is explained in Fatwa No. 71915. We hope that your prayer performed with tayammum is sufficient. We have clarified in Fatwa No. 100853 that many scholars permit issuing a fatwa based on a less preferred opinion after an event has occurred. By repeating the prayer, you have fulfilled your obligation, and there is no sin upon you for intentionally delaying the prayer until its time has passed. Rather, you delayed the making up of the prayer, which is a matter of scholarly disagreement regarding its permissibility. The Shafi'is permit it if the delay is due to an excuse, while the majority prohibit it, and their opinion is more cautious.