Dont uncheck checkboxs on update partial

Hello, I have a partial that returns a list of checkboxs so that the user can select ... And I have a text field for the user to include those not yet registered. When he sends this new value I update my list of checkboxs including one he sent. However, all checkboxs that are checked are unchecked.

I wonder if there is a way not to lose checkboxs checked ...

Sorry for my English...

Thanks