4 – Through al-Faḍl ibn al-Mukhtār, from Ḥumayd al-Ṭawīl, from him, in the wording: “A supplication is answered during the interval between the call to prayer.”
Al-Ḥākim recorded it in the same form as supporting evidence for the earlier narration of Sahl ibn Saʿd, and he remained silent about it—as did al-Dhahabī. Al-Faḍl, however, is discarded as a transmitter.

Notice: al-Shawkānī said: “The Prophet ﷺ specified what should be asked when he declared, ‘Supplication between the adhān and the iqāma is not rejected.’ They asked, ‘What should we say, O Messenger of Allah?’ He replied, ‘Ask Allah for pardon and well-being in this world and the Hereafter.’” Ibn al-Qayyim remarked, “It is an authentic ḥadīth.”

I say: Yes, the root narration is sound, but this additional wording is weak. Consequently, one may not claim that the Prophet ﷺ designated a particular supplication for this time. Take heed, and do not be among the heedless.

7 – The Iqāma
1 – It is a communal obligation, like the adhān, whenever a group prays—whether at home or on a journey—because of his ﷺ statement: “When the two of you set out, pronounce the adhān, then the iqāma, and let the older of you lead the prayer.”
This ḥadīth was recorded by al-Bukhārī—also in Al-Adab al-Mufrad—Muslim, Abū Dāwūd, al-Nasā’ī, and al-Tirmidhī.