Yes! Go to the “More” tab, and select “Download message archives”. You will be able to download the entire message history with you and any adult user. In self-service mode, you can download the archives involving you and any adult user, nobody else. Note that for privacy reasons, you can not request archives for message exchanges that do not involve you (e.g., between your co-parent and another family member) as they are private; nor can we pull messaging archives with a child under the age of 18.