How can I look up old or current text messages
How can I download text messages from a certain number
iPhone 11, 14
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There is no straightforward way to single out a number/sender and then download the text messages as you have stated. You may open the Messages app ➔ Type the name/number in the Search Field : This will display the text thread that you may be looking for. After that, there is no way to download the thread elsewhere and out of the Messages app. You may begin copy / pasting the messages in Notes if you like.
Axel F.