Step 1

Go on Facebook and click your profile picture in the top right.

Click Settings & Privacy

Settings

Then scroll down the left and click on Download your information

Enter your password and then click the Download or transfer information button shown below

Then select Specific types of information as shown below

Select Messages and click next

Press Next, selecting Download to device by default

On this popup, make sure to change Date range to All time and Format to JSON

Click Create files and wait approximately 1 day for the files to be ready to download

Step 2

When your files are ready to download there should be multiple files available to download. For me, the file containing the messages was 3/5, but it may vary.

Open the zip folder, it should be named something like : facebook-your-name19375

When you open the ZIP file, the first folder should be "your_facebook_activity", select that on the home page and enter the desired conversation name!