Is there a way that I can transfer a series of phone texts to my computer and make them into a Word or text file?

What device do you use? I use an Android phone and I can link it with my PC using my Microsoft account. I can copy my text and paste it onto a document.

Make an email account just for that. Set the email account in your phone contacts.
I have an email just for pics. When I want to send a pic from my phone I press “share” then type “pics” in the contact line. It autofillls all of the email info, then “send.”
So basically it’s just 2 clicks and a short type.

Digital Trends – How to save text messages in Android and iOS – “SMS Backup & Restore is a free app that does what the name implies. It can back up your text messages and save them locally on your Android device, export them to a computer, or upload them to an online storage service such as Google Drive”

Syntech – SMS Backup & Restore FAQs

For those of us in the Apple universe, any message I get on my phone is also available on my iMac. So I can copy by sender, and paste into any other app.

Its simple to do one or two, but if you want to save out thousands of texts from over several years you can find an app that supports it.

What OS is your phone?

I have an iPhone and use an app called iMazing. Not only can you control backups granularly, but you can export all the text messages, images, etc from messenger or other phone apps.