How to export text messages from an iPhone

Your options, from quickest to most complete

Screenshots: fine for a handful of messages. They show what was on screen and nothing more.
Forward or copy: press and hold a message, choose More, select messages and forward them. That sends the text as new messages, without the original times.
The Messages app on a Mac: with Messages in iCloud on, the history syncs to the Mac, where you can print a conversation to PDF. See exporting iMessages to PDF on a Mac.
A backup on a Mac: a backup made with Finder over a cable contains the phone’s messages, SMS included. An export app on the Mac can read it.

Why phone apps ask for screenshots

iOS keeps each app in its own sandbox. No app from the App Store can open the Messages database, so an iPhone app that promises to export your texts has to work from screenshots or screen recordings and read the text back from the images. That is why those exports tend to have dates but no exact times, and why they take as long as the scrolling does.

Export on a Mac with TextExhibit

Connect the iPhone to the Mac with a cable, or skip this if your messages already sync to the Mac.
Open TextExhibit and choose the source. For the iPhone, it makes a fresh backup on the Mac and reads the messages from it.
Pick a conversation and, if you like, a date range.
Export as PDF, CSV or HTML. Attachments are copied into the same folder.

What to keep in mind

You need a Mac with macOS 14 Sonoma or later. On Windows, see exporting iPhone texts on a PC.
A backup over a cable needs free space on the Mac and the iPhone’s passcode.
Exports show what is on the phone now. For deleted messages, see deleted text messages.

Questions

Is there a built-in way to export texts on iPhone?

No. iOS can back up, sync and forward messages, but it has no export or print option for a conversation.

Do I have to back up the whole iPhone?

A backup over a cable includes everything the phone backs up, not only messages, so it takes as long as a normal Finder backup. If your messages already sync to the Mac, you can skip the backup.

Which format should I choose?

PDF for a lawyer, a court or printing. CSV to sort and filter in a spreadsheet. HTML to read in a browser with photos. TextExhibit can write all three at once.