What is the ruling on completing the dhikr in prayer while starting the next posture, such as completing the dhikr of bowing or rising from it while starting prostration?

The basic principle is that the worshiper should recite the prescribed remembrance in its proper place and complete it before moving to another pillar. However, if he completes the remembrance while moving to another pillar, his prayer is valid according to some scholars, as a means of alleviating hardship. This is the view preferred by Sheikh Ibn Uthaymeen.