How to save a filtered View in a new sheet?

We are using a Master Smartsheet that contains all available project Tasks. Some of the Tasks have been nested (hierarchy) multiple levels deep.

When filtered we can then display the tasks required for a specific project. How do you save this filtered view to a new sheet and retain the nesting without the rows now filtered out?

I have tried copying and pasting whole rows and selecting cells, but I either lose the nesting or copy the rows that are hidden (not displayed) by the Filter that are not needed.