Move published components to branch without losing connection

Is is possible to move a published component to a branch, without losing the connection?

We have a local project component, that we want to move to DS library. But we agreed to work on branches in the DS. When the component is moved to the branch of the core library, the connection is lost. Is there a way to do it?

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Running into the same issue, we’re using Branching to manage contributions to our DS so when we need to move a component built in another file to the library branching breaks the connections.