Never used live mail but can highly rate thunderbird, have used this for years and syncs all my email accounts no problem, I only use it on my PC, I use Aquamail on my phone and tablet
I always find it better to use Imap accounts rather than Pop accounts when accessing them on various devices.
Is it hotmail accounts that you use? they probably mean you will still have the email account but just won't be able to use the program (Live) to open them, hence you need to use a new one like Thunderbird
- hope this helps
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