Based on current reports and search results, the claim that the King (Emir) of Kuwait has become Muslim is incorrect in its framing, as the ruling Al Sabah family in Kuwait, including the Emir, are already Sunni Muslims.
However, there is a recurring, unverified story circulating on social media regarding a Kuwaiti royal allegedly converting to another religion:
The Claim: A person identifying as Prince Abdullah al-Sabah has reportedly made audio recordings claiming to have converted from Islam to Christianity, expressing awareness of the risks involved, including death.
Context: This story has appeared periodically since around 2012, and often goes viral with claims of "shocking the world".
Verification: There is no official confirmation from the Kuwaiti royal family or credible news outlets that a prince named Abdullah al-Sabah has converted to Christianity. Some, including researchers quoted by La Stampa, have raised questions about the identity of the person on the audio recording.