How to split the part model along the same line

Hello
How do I go about making a single selection using Box/Lasso, then getting both the selection and its invert as two separate files? (by files I mean Model 1, Model 2, Model 3 etc)?

It seems like after I use Filter Selection (after selecting points via Box/Lasso), the selection that I made using Box/Lasso is gone i.e. I’m not able to get the other half of the selection through the same selection I made using Box/Lasso.