Open\move locked tab in new\exists lister

Hello.
I love DO.

Open\move locked tab in new\exists lister.

Locked tab opening in new lister:

  1. From tab menu: Click right-click on tab, select "Open in new lister". Opening new lister.
    Result tab is not locked.
  2. DragAndDrop (or move) locked tab on desktop. Opening new lister.
    Result tab is locked.

Locked tab move to exists lister:

  1. DragAndDrop (or move) locked tab from one lister to other lister.
    Result tab is not locked.

Can locked tab stay (or remain) always locked?
I use DO 13.4

13.4 is months out of date. Please update to the current version and link your account.

I try trial version.
I try current last version 13.6.2 beta.
изображение