OK gang. I have a shiny new SSD ready to install. i have suspended all tasks not already started, and will let running tasks finish to completion. As far as MW@home is concerned, what else do I need to do? Can I move the suspended task to the new hard drive? Should I abort them? The old spinning rust is coming completely out.

For me, I would run all tasks and make shure everything is uploaded and reported first.

If you stop BOINC and just clone the hard drive to the SSD, BOINC is none the wiser when you start it up again. Just un-suspend your cached work and proceed as usual.
If the new SSD is going to be a different system drive label like changing from C:\ to D:\ then you probably need to reinstall BOINC and go through the configuration where you tell BOINC where its DATA directory is located.

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Just clone the HDD
https://www.easeus.com/partition-master/clone-larger-hdd-to-smaller-ssd.html

. . . and you clone all the rubbish on the hard disk.

Its an easy to use piece of software. No fuss and can be done from w/in windows. If a user is asking those questions then something simple is needed. Copying 'garbage' and keeping the PC as similar as possible is probably more useful and easier to them then a clean install. Judging the question, credit and RAC this seems more like something in their capability.