Android - How do I turn off Messenger's default browser?
Go to messenger, go to Photos & Media and switch on: "Open Links in Default Browser"
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While this is a feature of the Facebook app itself, it appears there is no feature to do this with the current version of Facebook Messenger as of this answer (version 220.127.116.11.61).
The only current method in order to use the Android assigned default application for the URL is to Click the Menu Icon and click Open in ...
However if you are noticing that your in-app browser is slow, you may need to head into your Settings -> Apps and clear cache for Android System WebView and Google Chrome. (You may have to turn on Show System in the three dot menu.)
Not sure if you figured this out or not, or maybe they fixed it, but I figured it out. Open messenger. In the far upper right corner, tap the silhouette icon that takes you to your profile. Scroll down and check "open links externally"