To solve the problem of iCloud sync pausing iMessage, it is necessary first to ensure that the iPhone has stable access to the Wi-Fi network and enough battery power. The connection of the device to the power supply will enable the background synchronization process to proceed. Secondly, it is necessary to examine the iCloud storage, since a fully occupied account will not allow proper synchronization of Messages. In order to do this, one needs to go to Settings > your name > iCloud and see if the feature is turned on. It is also required to ensure that the iPhone uses the latest version of iOS. Read more: https://datarecovee.com/knowledge-base/syncing-with-icloud-paused/