You have a carmona, thé most difficult tree to keep inside. In the 6 years I am here I only have seen one person keeping it alive and thriving. This forum is literally filled with people asking for help for their dying/ dead carmona.
Our living rooms are just not suited to keep these plants alive, waaaaay to dry.
Concerning your question about the branches: a dead branch is, well, a dead branch, there is no way to revive something dead
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