My mother's laptop has been running as fast as a turtle on a snail going uphill for a long time now. Everything has been done to it, including formatting it and installing another, less cumbersome OS, but nothing improves. I have an HHD available, I have done some tests and it does work.
I hate to be "anti-environment and pro-capitalism", but... just buy a new one. The worst thing about HDDs (in my opinion) is that it's hard to tell when they'll fail. You don't have this problem. Clone the drive, spend $20-$50 on the same storage size, and you're done!
Or double the budget, and upgrade to an SSD. I know it's easy to suggest someone else spend their money, but that's really the only option here...
SSDs <1TB are competitive, if not outright beating, HDDs. You don't need to double the budget anymore. It might not be the fastest SSD at the cheap range, but the slowest SSD is still going to be faster than any (consumer grade) HDDs
Where I live (Venezuela) computer components are not very cheap or easy to obtain, and I don't have the money to afford an SSD (at least not now nor a near future)...