Is the worshiper, when prolonging the bowing (rukūʿ) or prostration (sujūd) during the night vigil (qiyām al-layl) prayer, obligated to recite all the invocations (adhkār) authentically reported from the Prophet, peace and blessings be upon him, or is it permissible for him to supplicate with any prayers (duʿāʾ) he wishes?

A worshiper may supplicate with whatever he wishes during his prayer, whether the supplication is transmitted [from the Prophet] or not, as long as it does not contain sin or severing of kinship ties. The positions for supplication in prayer are during prostration, between the two prostrations, and after the Tashahhud and prayers upon the Prophet (peace be upon him) and before the Tasleem. It has been narrated from the Prophet (peace be upon him) the encouragement to supplicate during prostration because it is the closest a servant can be to his Lord, and to choose the request and supplication he likes before the Tasleem. It is desirable to increase in supplications transmitted from the Prophet (peace be upon him), and supplication includes requests for this world and the hereafter, for oneself, for one's parents, or for others.