Is it true that the noble Hadith, the meaning of which is that if a man performs ghusl after having intercourse with his wife and then resumes intercourse, he is only required to perform wudu for prayer, and is what is mentioned actually permissible?

It is legislated for a man, if he has intercourse with his wife and then wishes to have intercourse again, to perform ablution (Wudu') as a recommended act, but it is not obligatory for him. This is based on the Prophet's (peace be upon him) saying: "If any of you has intercourse with his wife and then wishes to repeat it, let him perform ablution." The majority of jurists hold that the command in this Hadith indicates recommendation. If the one who wishes to resume intercourse takes a ritual bath (Ghusl), that would be better and purer, based on his (peace be upon him) saying: "This is purer and better." A ritual bath (Ghusl) is obligatory for anyone who wishes to pray after any intercourse.