This is a general question about submittal deadlines, In case we are doing split submittal, is there any rule that we have to submit the final design submittal before substantial completion date of the project construction ?
Nope. I've had projects all over the place with their LEED submission dates compared to the actual construction dates.
In general, it's better to keep the design submission close to the end of the design phases in case you need to make changes based on review comments. We all know that things happen in the real world, though, and it doesn't always work this way.