All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
We advise this person to be mindful of Allah and do his best to control his evil desires. Since his heart longs for prayer then he is a believing person who looks for repentance and pleasing Almighty Allah. It goes without saying that wine is the mother of all impurities, stains one`s heart every time he drinks it, and deprives him from happiness and contentment. It only causes him to lose in this life and the next.
As for the Hadith in which it is stated that the prayer of the person who drinks wine isn`t accepted for forty days, it is narrated by 'Abdullah bin 'Amr bin Al-'As (May Allah be pleased with them). 'Urwah bin Ruwaim narrated that : Ibn Ad-Dailami rode looking for 'Abdullah bin 'Amr bin Al-'As. Ibn Ad-Dailami said: "I entered upon him and said: 'O 'Abdullah bin 'Amr, did you hear the Messenger of Allah [SAW] say anything concerning Khamr?' He said: 'Yes, I heard the Messenger of Allah [SAW] say: If a man among my Ummah drinks Khamr, Allah will not accept his Salah for forty days." {Sunan an-Nasa'i 5664}.
This Hadith doesn`t indicate that prayer is prohibited for the one who drinks wine. Rather, prayer is an obligation upon him and he will be held accountable for it. However, the Hadith means that such person will not be rewarded for his prayer as a punishment for filling his belly with this impurity (Wine). Nevertheless, prayer is obligatory upon him and he is sinful for leaving it.
An-Nawawi (May Allah have mercy on him) said: "As for not accepting his prayer, it means that he will not be rewarded for it, even though it avails him and he doesn`t have to re-perform it." {Shareh Muslim, vol.14/pp.227}.
In conclusion, the above person must continue performing daily prayers on their time and stop drinking since, maybe, this prayer will be a reason for forgiving his other sins. And AllahThe Almighty Knows Best.