How to share leads between two users - lead generation and lead closing team?

How to share leads between two users - lead generation and lead closing team?

Hello,

We currently have two different kind of users :-

1) lead Generator
2) Lead closer

Leads module access is with 1)

and 

Leads module and Deals access is with 2)

In the Leads form, we have added a custom field called "lead closer" which is a user pickup list.

Same field has also been added in Deals form.

Now when we assign a lead closer using custom field and then hit convert lead > deals - we are loosing value stored in the custom field as it becomes blank.

Also as a result the lead closer can not access the record. So admin needs to assign it again to the lead closer.

Any solution for this scenario? How can lead sharing be implemented without losing record access upon conversion of lead into deals?