You can search Messages in the past in the following way.
<Desktop>
1. Click “Messages” on header.
2. You can search by entering keywords in search box.
3. You can search both “Subject” and “Body”.
<Mobile>
1. Tap “Messages” on footer.
2. Tap “Magnifying glass” icon on the upper left.
3. You can search by entering keywords in search box.
4. You can search both “Subject” and “Body”.