The hadith which the non Ahmadi Muslims quote is:
حَدَّثَنَا أَبُو الْيَمَانِ، أَخْبَرَنَا شُعَيْبٌ، عَنِ الزُّهْرِيِّ، أَخْبَرَنِي مُحَمَّدُ بْنُ جُبَيْرِ بْنِ مُطْعِمٍ، عَنْ أَبِيهِ ـ رضى الله عنه ـ قَالَ سَمِعْتُ رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ “ إِنَّ لِي أَسْمَاءً، أَنَا مُحَمَّدٌ، وَأَنَا أَحْمَدُ، وَأَنَا الْمَاحِي الَّذِي يَمْحُو اللَّهُ بِيَ الْكُفْرَ، وَأَنَا الْحَاشِرُ الَّذِي يُحْشَرُ النَّاسُ عَلَى قَدَمِي، وَأَنَا الْعَاقِبُ ”.
Narrated Jubair bin Mut`im:I heard Allah’s Messenger (ﷺ) saying, ‘I have several names: I am Muhammad and I am Ahmad, and I am Al- Mahi with whom Allah obliterates Kufr (disbelief), and I am Al-Hashir (gatherer) at whose feet (i.e. behind whom) the people will be gathered (on the Day of Resurrection), and I am Al-Aqib (i.e. who succeeds the other prophets in bringing about good). (Sahih Bukhari, Volume 6, Book 60, Hadith #419)
Firstly, this narration is unreliable. The narrators are:
al-Hakm bin Nafi’, Abu al-Yaman ——» Shu’aib bin Abi Hamza ——» al-Zuhri ——» Muhammad bin Jubayr bin Mut’im ——» Jubayr bin Mut’im
Now one of the narrators, Al-Zuhri, is not reliable at all. It is stated that “He would fabricate the odd time” (Mizanul-I’tidal, Volume 2, Page 146)
Another person who is considered a narrator is Sufyan Bin Uyaiyan and it is stted in regards to him:
“He would fabricate (narrations). Imam Ahmad sttes that this narrator has incorrectly quoted upwads of about twenty narrations from Zuhri” (Mizanul-I’tidal, Volume 1, Page 397)
“Yahya bin Sa’id Al Qattan statates that I testify on oath that Sufywan bin Uyaiyna completely lost his senses in 197 A.H. Hence anyone who takes a narration from his after this time it is unreliable” (Mizanul I’tidal, Volume 1 page 397)
It is also important to note that the words “after whom there is no prophet” to al Aqib has been added. Hazrat Mullah Ali Qari states:
“It is obvious that the words “and Al-Aqib is he after whom there is no prophet” have been added as a commentary by a companion or someone afterwards. Ibn Arabi states that Al-Aqib refers to someone whos ucceeds another person in something good”(Mirqat Sharh Mishkat, Volume 5, Page 376)
Another version which is quoted by some non Ahmadi Muslims is :
حَدَّثَنِي حَرْمَلَةُ بْنُ يَحْيَى، أَخْبَرَنَا ابْنُ وَهْبٍ، أَخْبَرَنِي يُونُسُ، عَنِ ابْنِ شِهَابٍ، عَنْ مُحَمَّدِ بْنِ جُبَيْرِ بْنِ مُطْعِمٍ، عَنْ أَبِيهِ، أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم قَالَ “ إِنَّ لِي أَسْمَاءً أَنَا مُحَمَّدٌ وَأَنَا أَحْمَدُ وَأَنَا الْمَاحِي الَّذِي يَمْحُو اللَّهُ بِيَ الْكُفْرَ وَأَنَا الْحَاشِرُ الَّذِي يُحْشَرُ النَّاسُ عَلَى قَدَمَىَّ وَأَنَا الْعَاقِبُ الَّذِي لَيْسَ بَعْدَهُ أَحَدٌ ” . وَقَدْ سَمَّاهُ اللَّهُ رَءُوفًا رَحِيمًا .
Jubair b. Mut’im reported on the authority of his father that he heard Allah’s Messenger (ﷺ) as saying:I have many names: I am Muhammad, I am Ahmad, I am al-Mahi through whom Allah obliterates unbelief, and I am Hashir (the gatherer) at whose feet people will be gathered, and I am ‘Aqib (after whom there would be none), and Allah has named him as compassionate and merciful. (Sahih Muslim Book 43, Hadith #164)
The true meaning of Al Aqib has already been mentioned by Mullah Ali Qari and Ibn Arabi, which further shows that these ahadith have nothing to do with the closing of prophethood.