Parallels virtual machine was migrated using a VMware virtualization product. Parallels Tools were installed on the resulting VM, and the mouse synchronization feature worked well. After a period of time, VMware Tools were removed from the machine, and mouse synchronization stopped functioning properly: mouse cannot be seamlessly moved between host and quest operating systems, and it is impossible to switch to Coherence mode.
When VMware Tools are removed, the driver for the Parallels Mouse Synchronization device is also deleted.
There are two possible solutions:
1) Reinstall Parallels Tools as advised in KB 4841.
2) Reinstall the driver for the Parallels Mouse Synchronization device (for Windows virtual machines only):
Start VM, click on Start > Control Panel > System > Hardware > Device Manager. In the opened snap-in, select Mice and other pointing devices. Choose the available mouse device (probably Microsoft PS/2 Mouse) and double-click on it.
In the Properties window on the Driver tab, select Update driver > Install from a specific location > Do not search.
In the list of available drivers, highlight the Parallels Mouse Synchronization driver and proceed to installation. After the virtual machine reboots, mouse synchronization should work as designed.