Praise be to Allah.
Al-Bukhaari (may Allaah have mercy on him) said in his Saheeh:
Chapter on a slave or freed slave leading the prayer: Aaishah used to be led in prayer by her slave Dhakwaan whilst he was holding the Mus-haf. (Saheeh al-Bukhaari, Kitaab al-Adhaan).
Ibn Hijr (may Allaah have mercy on him) said inFath al-Baari Sharh ala Saheeh al-Bukhaari (his commentary on Saheeh al-Bukhaari): The phrase Aaishah used to be Abu Dawood completed the chain of narration in Kitaab al-Masaahif, via Ayyoob from Ibn Abi Maleekah, who said that Aaishah used to be led in prayer by her slave Dhakwaan whilst he was holding the Mus-haf (the Quraan). The chain of narration was also completed by Ibn Abi Shaybah, who said: Wakee told us from Hishaam ibn Urwah from Abu Bakr ibn Abi Maleekah that Aaishah freed a slave she owned he used to lead her in prayer during Ramadaan, holding the Mus-haf.
If the imaam or a person who is praying alone recites from memory, this is better, but if he reads from the Mus-haf, there is nothing wrong with it. And Allaah knows best.
* (Translators note) Mus-haf: a written or printed copy of the Quraan.