Phpbb3 ajax mod needs to be developed.
This would be done with extjs + json + php ( if you can suggest any other ajax framework, let me know).
Database layer code and database model can be taken from phpbb3.
You need to develop very good JSON layer ( so that later it could be used with any other framework/client etc..). At first, UI will be developed with ExtJS.
There's extjs forum example ( download extjs-2.0.2 and see under examples/ directory), which can be used as base to on which to develop this project.
In this project what I need you to do is :
1) Add message posting.
2) Add login/logout/show login status
3) Develop JSON layer that supports all neccesary features ( login/out, posting, forum lists, message listing by pages, and of course must follow phpbb3-s ACLs. Also this must be developed in scalable style, so that it would be easy to extend its functionality later ).
I expect you to provide well designed (OOP) code, with good documentation. Every variable/function/function block must be well documented. Functions must be short and clean as possible.