You need only:
1. Buy new VM Invoice
2. Download it (It will enable new license)
3. Use your new download id in configuration of VM Invoice
4. Update via VM Invoice Update page

I agree that backup should be always made for sure.

We've upgraded VM Invoice version but special characters are still not visible. We really need to send loads of invoices, could you please tell us how to fix this problem? Thank you.

I've checked the whole site once again trying to remember if there were any significant changes we made recently and I realized that we've added more languages to Frontend (VM translation is done with JoomFish). Could this be the problem? If so, how do we ensure that invoices are created in default site language (which is not English)?

Hello,

Can you send me admin access to your site to Tato emailová adresa je chráněna před spamboty, abyste ji viděli, povolte JavaScript ?
I will consult it with developers.

Thanks for the effort but we experimented with various options and discovered that problem with special characters exists in FF but not in IE. So, we're processing invoices in IE, and doing the rest of the work on our website in FF. However, it would be good to have this issue resolved in FF.

Then it looks more like browser plugin problem. Result of TCPDF would be always same and there doesn't matter if it is printed in IE or FF.