Is it permissible to liken the current president of Egypt to the Prophet of Allah, Yusuf (peace be upon him), given that he was released from prison and assumed power, with mention of evidence for permissibility or prohibition?

What the Sheikh said about resemblance is not objectionable if the point of resemblance is clarified. It was used by theaf (pious predecessors). In the story of Abu Muslim Al-Khawlani, Omar (may Allah be pleased with him) said: "Praise be to Allah who did not take my life until He showed me, among the Ummah of Muhammad, someone who was dealt with as Ibrahim the Khaleel was dealt with." Scholars approve of Jarir's saying: "He attained the caliphate as it was destined for him, just as Moses came to his Lord by destiny." The Prophet (peace be upon him) also said to Ja'far ibn Abi Talib: "You resemble me in my physical form and my character."