This is done with this mod (Advanced Application Forms), you have this option in AdminCP.
Go to
Application Positions, choose position you want to have applications created in thread as new posts.
Use this options:
Report in Existing Thread set to yes
Existing Thread ID you need to have this thread already created, but this isn't problem. ThreadID is number with which vB describes thread, you can get it from link of that thread.
For example, this is link from your forum:
http://www.immihelp.com/forum/showthread.php?t=96101
I bolded and colored thread ID. Of course, you can create any new thread and anywhere, just take thread ID and put it there.
Poster ID - You could use this, or not (I leave it at 0).
Anyway, look at instructions what every option does, it's explained in detail.
Also note that in the same time you could use more options simultaneously i.e. you could create new thread, post new post in existing thread, post PM, send e-mail... Check options and decide what suites you best.