Smartwatches have gained significant popularity in recent years. One major use of smartwatches is notification checking as an extended display. Smartwatch use provides an opportunity for energy saving because it affords a reduction in the frequency of smartphone use. However, sometimes user input is limited in smartwatches due to its small screen size and users are forced to use their smartphones to fully read notifications. In such cases, the advantage of an extended display in the smartwatch diminishes because users need to access their smartphones, which causes extra smartphone battery consumption. We define phone-preferable notification that requires a user to take further actions, such as checking detailed content and replying to a message. Given that phone-preferable notifications are likely to be handled on smartphones, it is possible to defer notification delivery to smartwatches. In this paper, we develop a novel notification manager, called PASS that automatically defers phone-preferable notifications and piggybacks them on watch-preferable notifications. For model building and evaluation, we collect 15,659 notifications in-the-wild from 11 users for approximately 31 days. In addition, for approximately two months we gather self-reported data from five users regarding which devices were used to respond to notifications. The results show that PASS can save daily battery for smartwatches and daily battery for smartphones up to 43.5 and 0.9 percent without introducing any noticeable negative results on user experiences.