How to avoid duplicating when inserting both lines at once

Question

Hello friends first I will explain the state after I will give you my need

I have a datagridview with a checkbox I check the lines after I click on the "save" button and normally the lines I check they will have to be inserted both in the other table but I find that just one line that was Insert twice

The second problem is that I want the lines I inserted I want the most to see when I click on the search button because there are already assigned in the table

You will find  the two interfaces that process the state

I hope I have described my condition well and thank you in advance