For the record, in UE 4.25 setting Project Settings > Runtime Navigaton to “Dynamic” and using “RebuildNavigation” console command (either in BP or C++) after moving navmesh does the trick - navigation is rebuilt after navmesh volume is moved.
EDIT: executing console command with ExecuteConsoleCommand BP node always works, but for me only
UKismetSystemLibrary::ExecuteConsoleCommand(GetWorld(), "RebuildNavigation");
worked in C++.