This argument was presented in The True Meaning of Khatame-Nubbuwat, an Urdu speech by Mirza Tahir Ahmad translated into English, on page 40.
34. And Joseph, indeed, came to you before with clear proofs, but you ceased not to be in doubt concerning that which he came to you till, when he died, you said, 'Allah will never raise a Messenger after him.' Thus does Allah adjudge as having gone astray every transgressor, doubter -
35. Those who dispute concerning the Signs of Allah without any authority having come to them from Allah. Grievously hateful is this in the Sight of Allah and in the sight of those who believe. Thus does Allah set a seal upon the heart of every arrogant, haughty person.
- Muhammad ‘Ali translation
Ahmadi Argument
The concept of the finality of prophethood was attempted by the people of Pharaoh. In response to this belief, Allah says that those people who dispute concerning the signs of Allah have said something grievous and hated in the sight of Allah and the believers. This is the exact same belief of the Muslims of today. They believe that after the Prophet Muhammad, there will be no more prophets. However, Allah said in verse 35 that this is a hated belief.
Muslim Response
If one reads from verse 28, it is clear that this is a believing man speaking.
28. And a believing man from among the people of Pharaoh, who kept hidden his faith, said, 'Will you slay a man because he says, 'My Lord is Allah,' while he has also brought you clear proofs from your Lord? And if he be a liar, on him will be the sin of his lie; but if he is truthful, then some of that which he threatens you with will, surely, befall you. Certainly, Allah guides not one who exceeds the bounds and is a great liar;'
29. 'O my people, yours is the sovereignty this day, you being dominant in the land. But who will help us and protect us from the punishment of Allah if it comes upon us?' Pharaoh said, 'I only point out to you that which I see myself, and I guide you only to the path of rectitude.'
30. And he who believed said, 'O my people, I fear for you something like the day of destruction of the great peoples of the past;
31. 'Like that which happened to the people of Noah, and the tribes of Ad and Thamud and those after them. And Allah intends no injustice to His servants:
32. 'And O my people, I fear for you the day when people will call one another for help,
33. 'The day when you shall turn back fleeing; and there will be no one to save you from Allah's wrath. And for him whom Allah leaves to go astray, there shall be no guide.'
From verse 28 to 34, all of these are quotations of the believing man who is speaking to the people of Pharaoh. He is warning them of all of the terrible things that could befall them just as they befell the people of the past. Then, in verse 34, he says, “At length, when he died, ye said, 'No messenger will Allah send after him'.” The believing man says “you said”, referring to the people of Pharaoh. One can conclude that it was the people of Pharaoh who originally said, “No Messenger will Allah send after him.”
Then, in verse 35, Allah explains that this statement was not hated merely because it was an incorrect statement. As is stated in the next verse, the explicit reason given by Allah is that these people had no authority[1] over the religion of Yusuf. They did not believe in the religion of Yusuf, nor did they receive any revelation from Allah to speak on its behalf.
This is an attempt by the Ahmadis to insert their beliefs where they do not exist. The Ahmadi argument fails when one looks at the full context of the ayah.
[1] سلطان means authority in the sense of having a right over something or someone. In context, the people of Pharaoh had no right over the religion of Yusuf.