As far as I know there is no Exchnage 2019 trial so I can't check it out by myself.
The latest CUs of Exchange 2019 are available in the below links, which you can download for test.
Exchange 2019 CU10
Exchange 2019 CU11
Below are some links about the hardware requirements, prerequisites and compatibility (clients,AD,etc.) of Exchange 2019, which you may need to take into consideration before install.
Exchange Server system requirements
Exchange Server prerequisites
Exchange Server supportability matrix
And since you are using SBS 2003 (Exchange 2003), you cannot migrate to Exchange 2019 directly.
To migrate from Exchange 2003 to Exchange 2019, You may need to:
- install Exchange 2010, migrate to Exchange 2010
- install Exchange 2013/2016,migrate to Exchange 2013/2016
- install Exchange 2019, migrate to Exchange 2019
Here is also a link about the similar question for your reference: how to migrate exchange 2003 to 2016 including active directory renaming please help
However, in this case it may take a lot of effort.
A workaround would be migration with export/import pst files via Outlook.
You may simply setup an Exchange 2019 server and create mailboxes on it.
Then import the pst files into these mailboxes.
Export/Import pst files via Outlook: Export or backup email, contacts, and calendar to an Outlook .pst file
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Back to your question, did you mean the users have two mailboxes?
One is hosted by Exchange 2003 and the other is hosted by one external mail server. And the Exchange mailbox is only used for storage.
In case of local PC loss/failure new Outlook installation download all the mail from sbs 2003 to local PST, automatically.
In my opinion, it should work the same way for you.
However, there are also many factors you may need to take into consideration.
For example, Outlook compatibility as mentioned above.
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