You should look into a FileMaker hosting provider, such as ourselves:
We supply the server, FileMaker Server Advanced license, monitoring, maintenance, upgrades, etc. so you don't have to maintain your own server. You can access your databases via any combination of FileMaker Network Sharing (FileMaker Pro <-> Server), Instant Web Publishing, Custom Web Publishing (XML/XSLT, PHP or Lasso) and/or ODBC/JDBC. We supply 25 user connections with all of our shared hosting accounts.
We have been providing Professional FileMaker Hosting for over 11 years. Feel free to let me know if you have any additional questions either here or off-list to jmay(at)pointinspace.com.
You can share a database with a dynamic IP address.
Though dynamic, they often change very infrequently.
You can check this with http://whatismyipaddress.com over a week or so, with computer shut downs.
If the power goes out, this is the most likely time the IP address might change.
You would just let him know the new IP address.
If it does change frequently, there is a free service to help http://www.dyndns.com/services/dns/dyndns/
Assuming you both have high speed internet connections and both have Filemaker.