Your best bet is to use a dynamic DNS service to allow your customer's employees to find his server. Your customer's server will run a small program or script that reports IP address changes to the dynamic DNS server, ensuring that DNS always has up-to-date information.
There are several dynamic DNS providers offering services for free or a nominal fee. If your customer doesn't already have a domain and doesn't want to get one, some services, such as DynDNS, will provide one for him.
Dig Deeper on Network management services
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