Hi,
For windows server backup in external drive, if you connect to another host. The backup feature (WSB) in the new host should also recognize it. And when you choose restore, it should shows the backup version to restore.
And in case of something wrong, you could also do a test in your environment.
Here is a reference:
http://www.iperiusbackup.net/en/restore-hyper-v/
Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information. For the 3rd party backup software mentioned in the article, couldn't find from the Microsoft site, may need to contact the vendor.
In addition, it is more recommended, if you need to restore to other host, the different host with the same hardware configuration.
And sometimes, different hardware characteristics may cause VM with saved state. Here is the related KB. As suggested above, you could consider to do a test in your environment.
https://support.microsoft.com/en-us/help/2502233/restored-hyper-v-virtual-machines-won-t-start
Best Regards,