Regardless of whether you are in the Texting or the Teams area in Speak, you'll always have a "Search messages" area at the top of the page:
You can use this search box to search for specific words, phrases, etc., that show up in any of your text messages to contacts or in your chat messages in your channels or direct messages. All instances of the items you are searching for will display in the main Speak pane after typing in your desired search text and hitting Enter. For instance, let's say we searched for "paperwork" using the "Search messages" box. We might see the below:
Note that we're seeing results from a Team Channel, Direct Message rooms, and a Client Inbox. Note as well that the word or phrase you search for will be highlighted to make it stand out.
If you hover your cursor over a particular message, you'll see an option to "Show Context":
If we click that "Show Context" option, we'll see a popup window displaying the message in the context of the conversation that occurred around it:
As your historical text and chat conversations grow, you'll likely find this "Search messages" option a huge timesaver when attempting to track down conversations if you can't recall exactly when they occurred.