Is forgetting a raka'ah in Dhuhr prayer, then performing the prostration of forgetfulness (sujud al-sahw) and concluding the prayer (tasleem) a correct action, or must the prayer be made up after a long time has passed?

If a worshiper forgets a rak'ah in the Dhuhr prayer and remembers it before starting the recitation of the next rak'ah or before performing its bowing (ruku'), he should return to it and perform it. If he does not remember it until after that, then the subsequent rak'ah takes the place of the forgotten one. He should then perform an additional rak'ah after finishing the prayer and before the salutations of peace (tasleem), and then perform the prostrations of forgetfulness (sujood as-sahw). However, if he does not remember it until after he has finished the prayer, he should perform the forgotten rak'ah as long as the interval has not been long or his ablution (wudu') has not been invalidated. Otherwise, the prayer is void and must be repeated. Consequently, if a long time passes after forgetting a rak'ah without performing it and only performing the prostrations of forgetfulness, then the prayer is invalid and must be made up (qada'), because a rak'ah cannot be compensated for by the prostrations of forgetfulness alone.