Short answer: sometimes, but not magically and not always for free.
If the history is cleared, a simple browser add-on usually can’t recover old data. What you can do is:
- Install a monitoring app on their device that logs future browsing/searches before they’re deleted. These work at system level, not just in the browser.
- Check router logs or your Wi‑Fi admin panel if you control the network (some routers keep a basic history).
- Avoid pricey, overcomplicated “forensics” tools unless you really need deep recovery.
If you go this route, read up on local laws and think about what you’ll do with the info before you start.