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
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…