Yes, put this in the notes.ini file on all the client machines you use:
This will synchronize unread marks once every 8 hours. This can slow down replication a lot and only works on Notes 4.13, 4.51 and higher. The problem is fixed in Notes 4.6 and above, so you won't need this setting.
Another technique the user can use is the following:
1) Unstack the replica icons under the view menu.
2) Select the two databases on the workspace by clicking w/ the Shift key depressed.
3) Choose Edit/UnreadMarks/ExchangeUnreadMarks.