Cutting a Mac loose from Portable Home Directory
A high level approach to make the network account on the server as a local account on the MacBook Air would be to do the following:


Unbind the MacBook Air from the directory and delete this user from it.
Copy over the user's home folder from the server into /Users/ on the MacBook Air.
Create a new user with the same shortname as on the server.
Choose OK when OS X prompts you asking if you'd like to use the already existing home directory for this user. This will fix the permissions on all files for this user.