Is it permissible to raise one's hands when supplicating after the Adhan (the call to prayer) with the words, "O Allah, Lord of this perfect call"?

There is no objection to raising the hands when supplicating after the Adhan; in fact, it is recommended. As stated in the Hadith: "Whoever says when he hears the call [to prayer]: 'O Allah, Lord of this perfect call and the standing prayer, grant Muhammad the Wasilah (a station in Paradise) and the Fadilah (a rank of superiority), and raise him to the praised station that You promised him,' my intercession will be due to him on the Day of Resurrection." The time of the Adhan is one of the occasions when supplications are answered. The Messenger of Allah, peace and blessings be upon him, said: "When the Adhan is called, the gates of the heavens are opened, and supplications are answered." Raising the hands during supplication is recommended, except in cases where the Sharia has made an exception, such as supplication during the sermon or prayer outside of Qunut.