After the question arose on the Seti message boards I thought I would post the process I used to upgrade all my Intel iGPU machines from Debian Jessie to Debian Stretch. For each one of them I did the following process to copy the BOINC data folder and put it back when done.
I'm running Debian so it should work for other distributions that are based on Debian (such as Ubuntu). This assumes you've used the repo version of BOINC. If there is also a BOINC version upgrade happening then you should be careful about point 12 below.
1. Set BOINC to no new tasks. I usually let it complete any tasks in progress.
2. Login as root
3. Stop BOINC - in a terminal window type "service boinc-client stop" without the quotes
4. Insert empty thumb drive into a USB port. This brings up a window on the desktop showing the contents.
5. Using the GUI copy the contents of /var/lib/boinc-client to the thumb drive. I click on the computer icon, navigate to the folder, click on a single file, Ctrl-A to select all files and drag it over to the thumb drive window. Just like Windows.
6. It complains about can’t copy sym linked files so navigate to /etc/boinc-client select all the files (there are usually four) and drag and drop them on the thumb drive window as well.
7. Install new OS
8. Login as root and install repo version of BOINC.
9. Stop BOINC.
10. Insert thumb drive again
11. Using the GUI copy the files back to /var/lib/boinc-client
12. Copy the /etc/boinc-client files back separately using the GUI. They are sym linked from /var/lib/boinc-client. They get put there by the repo install so overwrite them with your version from the thumb drive. I just drag and drop them one at a time.
13. In a terminal window cd to /var/lib/boinc-client and change permissions back to user boinc (type "chown boinc:boinc * -R").
14. Start it up (in a terminal window type “service boinc-client start”) and it resumes from where it left off.
For a new version of BOINC all I do is install it by login as root, start a terminal session and type "apt update" followed by "apt upgrade". It will stop BOINC, install the new version and start it up again. You can even do it via ssh (remote login) if you want.