How to use WebDAV to access mailboxes across Exchange servers?
If there is a front-end server setup, you can access by opening a connection using HTTP or HTTPS and to WebDAV they would seem seamless - i.e. one server. This is what I have seen used almost all of the time.
Using Microsoft Exchange 2000 Front-End Servers
You may also be able to access a server using <\\.\BackOfficeStorage>. This path only is good for the Exchange server where the code must be running from. The <\\.\BackOfficeStorage> path is not normally used with WebDAV and it is what the M: drive is mapped to on Exchange 2000. The M: drive is not mapped to this with Exchange 2003. Accessing files directly with file system access through the M: drive or <\\.\BackOfficeStorage> is not supported. I see this method used for access using CDOEX/ADO most of the time and almost never for WebDAV.
XADM: How to Use \\.\ Namespace to Gain Access to the Information Store
https://support.microsoft.com/?id=239743
The File: URL Scheme
https://msdn.microsoft.com/library/en-us/wss/wss/_exch2k_the_file_url_scheme.asp?frame=true
Accessing two mailboxes on two different servers with WebDAV should use the same path that you would enter into OWA for accessing them from the web using IE. What you would use for an HTTP/HTTPS path is a matter of Exchange and domain configuration.
Getting the Host Domain Name
https://msdn.microsoft.com/library/en-us/wss/wss/_exch2k_getting_the_host_domain_name.asp?frame=true
The HTTP: URL Scheme
https://msdn.microsoft.com/library/en-us/wss/wss/_exch2k_the_http_url_scheme.asp?frame=true