Ok, seems its not so hard,
- I've placed the PunBB.NET in my app subfolder
- changed links to master pages and links in sitemap's files
- merged web.config's
- set the default membership provider in web.config to my app membership provider
Now when I login in my app login form, - I can enter the forum and it recognizes me as already logged in user.
I can even create topics, but they are not shown in the topics list, probably because of they are stored in the database without UserId, which has a different type in the base membership table (uniqueidentifier vs varchar(200)).
But this should not be a big problem to fix it.