A-Frame systems are among the most efficient order picking devices. Stock keeping units are stockpiled in vertical channels successively arranged along an A-shaped frame and a dispenser automatically flips the bottommost item(s) of each channel into totes or shipping cartons that pass by under the frame on a conveyor belt. Although order picking itself is fully automated, continuously replenishing hundreds of channels still remains a laborious task for human workers. We treat the research question: if the sequencing of picking orders on the A-Frame can facilitate the replenishment process. In many real-life applications, workers are assigned to fixed areas of successive channels, which they have to timely replenish. Our sequencing approach, thus, aims to properly spread the replenishment events of each area over time, such that each worker has sufficient time to move from one replenishment event to the next. We formulate the resulting order sequencing problem, consider computational complexity, and suggest suited heuristic solution procedures. In our computational study, we also apply a simulation study of the replenishment process to explore the gains of our approach.