Mu`awiya bin al-Mughira

Muʿāwiya ibn al-Mughīra ibn Abī al-ʿĀs ibn Umayya was a member of the Banu Umayya alleged to be a spy against the Muslims during the time of the Islamic prophet Muhammad. He was captured during the Invasion of Hamra al-Asad, where Muhammad accused him of being a Meccan spy, he was the cousin of Uthman ibn Affan, had been captured after Uhud. Uthman gave him shelter. He was given a grace period of three days and arranged a camel and provisions for his return journey to Mecca. Uthman departed with Muhammad for Hamra-al-Asad, and Muawiya overstayed his grace. Though he fled by the time the army returned, Muhammad ordered his pursuit and execution. The orders were carried out.[1][2][3][4][5]

This incident is also mentioned in Ibn Ishaq and Ibn Hisham's biography of Muhammad.[6]

https://en.wikipedia.org/wiki/Muawiya_ibn_al-Mughira

What was the relationship between Muawiya and Muhammad?

Unlike his predecessors, who had been close, early companions of Muhammad, Mu'awiya was a relatively late follower of the Islamic prophet. Mu'awiya and his father Abu Sufyan had opposed Muhammad, their distant Qurayshite kinsman and later Mu'awiya's brother-in-law, until Muhammad captured Mecca in 630.
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Mu'awiya I - Wikipedia