Is it permissible for someone who missed the Isha’ prayer to pray Witr with the Imam who intended three rakahs without a separate shaf?

The Witr and Qiyam prayers are only performed after the 'Isha prayer. Their time begins upon finishing the 'Isha prayer and extends until dawn. If a person enters the mosque late while the Imam is performing the Tarawih prayer, it is permissible for him to join the Imam with the intention of praying 'Isha. He then completes his prayer after the Imam performs the Taslim, and then he continues with the Imam for the remainder of the Tarawih prayer.