1. Open an elevated command prompt: Click start, type CMD

2. Run: psexec.exe \\<localServerName> /s yourapp.exe
This will provide you with a new command prompt, but it will instead run under the SYSTEM context, instead of your user context.

3. Run: net use \\<remoteServerName>\<sharename> /user:<domain>\<userName> <password>
This authenticates the SYSTEM account to the share you want to export to.
As an example, the line could look like: "net use \\server2\c$ /user:mydomain\Administrator MyAw3s0m3Pwd"

4. Return to the Hyper-V MMC, and try your export again.  It should work now.

5. When you're done, use: net use \\<remoteServerName>\<sharename> /delete
This revokes the credentials from the SYSTEM account. 
Alternatively, you could reboot.