Sheikh `Abdul-Majeed Subh, a prominent Azharite scholar, states: “While performing Prayer, at least one has to move his lips with the recitation according to the Maliki school of Fiqh. According to Shafi`i school and other Muslim jurists, while performing Prayer one has to recite with a voice the lowest of which is to let himself hear his recitation.

As for offering the Obligatory Prayer while making recitations in his mind, his Prayer is invalid because recitation is one of the pillars of Prayer bearing into consideration that reciting or reading indicates moving the lips with the recitation.

As for saying Allahu Akbar in Prayer, if you mean the opening takbir (takbirat Al-Ihram), it is obligatory to move the lips with reciting the opening takbir because it is obligatory as well as the concluding taslim. As for the other takbirs during the Prayer, they are sunnah and not obligatory.

Having stated the above, it becomes clear that one has to move the lips with the recitation during Prayer.