How do I update my phone number on Messenger?

I do not have a Facebook account, but run Messenger through my mobile number. I need to get a new phone number but can't work out how to update this on Messenger so that I can have my conversations and groups through my new phone number. 

I previously had issues where Facebook thought my number was linked with an existing Facebook account and it deleted my messenger account that I had created with my mobile number and it deleted all of my groups and conversations, so I'm looking to avoid having to start all over again.

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