Gmail does not support sending files bigger than 20MB. this can happen in other email clients as well
Solution 1: Choose HTML as the export format
HTML is a much smaller file and if the file is still too big you can split it into multiple files (see solution #3 for instructions)
Solution 2: Share via Google Drive
Instead of gmail (or any other app), choose "Save to Drive"
Scroll through the notification tray from the top - you will then see the upload progress of the file. When the file is fully uploaded to Drive, click on the notification
Press the icon with 3 dots located next to the conversation file
Turn on "Link sharing" and press "Copy link"
Open your email app, write a new mail and paste the link in the mail body.
Solution 3: Split the file into multiple smaller files
In the "sharing methods" option, click on settings icon next the the selected format
- Turn on "Split Files"
- Choose how many messages in every file
- Save (on the top-right corner)
Solution 4: Connect your desktop computer to your phone via USB
You can transfer the files to your desktop via USB.
Just connect your phone and browse to "SMS Backup/Conversations" directory in your phone's internal memory