Are there any switchboard applications? I'm looking for an application that converts my Android phone in a switchboard. The goal is to have the ability to redirect the incoming calls to another telephone number. But if this is not possible (I don't know if any Android terminal is able to redirect calls in real time), perhaps there is an intermediate solution: the mobile pick up the telephone, launches a recorded message ("Please, say what is the purpose of your call"), waits until the user say something and then put a music loop until somebody pick up the telephone.

I don't know if I explained :) But the final goal is to substitute an expensive internal switchboard by an unexpensive cell phone network driven by an Android app. Is there something similar?
I was looking for something similar and it is hard to find one that would work for android.

However it is not so expensive to have a really good phone switchboard, you may use a very old computer with phone modem and utilized the land line, for example you can get an almost-for-free, an old PC computer from garage sales or bank or company that is in the process of updating their IT systems, (like a Pentium II or III).

Then install either Windows XP or Linux along-side with a PBX server which you can download for free for both systems. Sure it will take a little bit of time and patience to configure, the end result will be worth it, if done properly.

A switch-board that will change a PC at your office to a desk phone. Even, you can also have a intercom facility as well (where users can call each other without using land line just over your LAN - just PC to PC), even you can join remote branches or offices into one phone system. 

Then you can have internal numbers like 1214 or of your own preference and choice, and share the one line over many users, and the most beautiful part is that there's no need to make new wires and getting phone sets! 

Search google for 3cx (for windows) or Asterix for Linux.