You can forward the text message to an email address and print from a computer. Generally most of our plans include unlimited text messaging, if you do not have a plan of this type the charge for the text is include on your bill. Are you trying to get the number of texts you used for work versus personal text messages?
You would have to forward the text that have to do with business to an email address that you can access on a computer and download them that way you could both keep track of how many messages were business related and have the documentation to submit for your work. Sprint has not kept a an online copy of text message since I have been with the company. I know this is not the easy way of dealing with the issue
Check out a fun infographic that teaches you how to increase storage, enhance security, improve battery life and clean your device.