@RobertoS - apologies for hijacking the thread a little
No problem, the whole thread has been most informative.
@ (in order of first contribution) ggremlin; AEP; XRaySpex; nredwood. I read up about IMAP again, and it has developed a fair bit since I looked at it quite a while ago - I hadn't realised that might happen as I thought it was just as old as POP3 and just as fixed.
Allied to the facts that I don't remember which email client I was using when I investigated it, and maybe Purple Cloud server not Tsohost, and if it was Tsohost their implementation may have been upgraded, I was well out of date as to what could be achieved with it. Whatever the reason, maybe even I got hold of the wrong end of a stick, it wasn't suitable when I originally checked it out. I think it was to do with synchronisation, in particular the "Sent" folder.
Anyway I have set up a single IMAP account in Thunderbird on the W7 machine and added one on this machine, and so far things look hunky-dory. In particular the "Sent" folder seems to be reflecting onto both machines as well as the obvious Inbox.
So I shall make sure I don't lose anything and set about re-arranging the accounts and filters I have here, on the Tsohost server. They could do with a bit of rationalisation anyway. Probably start afresh on the server and stick all the existing email in an umbrella folder (say Local Folders) with the existing structure under it, on both machines, for searching purposes, as we use that a lot.
I must admit at the moment to be slightly confused as to whether I am looking at the server Inbox or the local Inbox when online. I'm pretty sure it is the local. The setup I have is downloading the full server contents, folders and messages, which is fine, as I have a network security disk so can periodically delete from the server as I don't have a huge amount of space there. Next experiment, delete something here and see what happens, and delete something on the server and see what happens. Don't tell me

.
Thanks again, all the above.
@normcall - I hadn't really considered the network drive I have, which is basically for Acronis backup, but I suppose I could have used that. Possible complications as have been mentioned, and also the fact it's onsite so at risk of disappearing if we have a burglary. It has several times proved very useful in recovering data though. I need to rethink backups!
@BatBoy - nothing against Exchange but so far as I'm aware it's very expensive, and doesn't it require MS email clients, at least on Windows machines? Live Mail doesn't cut the mustard for me and Outlook again costs. I asked about clients a fair while ago and was talked into the excellent Thunderbird after I'd initially rejected it due to complication and a couple of minor niggles.
@dandnsmith - interesting re VPOP3, but I think the IMAP solution suits me, and VPOP3 does cost. Pegasus was one of the clients I considered before choosing Thunderbird. It nearly fitted my wants but TB is closer. Thanks for the suggestions though.
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost.
Internet connection - IDNet Home Starter Fibre.
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"Where talent is a dwarf, self-esteem is a giant." - Jean-Antoine Petit-Senn.