In some Android phones, while viewing the text thread you want to save, there is a tri-dot menu at the top right. If you click it, some phones have an option to "save" the texts in an office file in your phone's documents. From there you can either e-mail it to yourself, add it to an online cloud drive, or directly transfer it to your computer. DO NOT DELETE the ones in the phone until you know you have a legible format in multiple copies for your records. (Army advice)