iExplorer will display the full text message history that is on your device at the time of backup, and there is no limit for how far back the text history can go. As long as it’s on the device, then iExplorer can display it and export it.
For the older, missing segments of the conversation, do you definitely see the full conversation in the Messages app on your device? Or, are you looking for deleted texts? If you are looking for deleted texts, please see the article below:
How to recover deleted iPhone text messages