If it is the X3AP Corporation Troubles mission chain, then according to
walkthrough the end requires:
1. Comm the designated Stock Exchange
2. Comm the designated Shipyard
3. Choose a Corporate Headquarters style
4. Dock a TL with at least 10,500 space at the designated shipyard
5. Collect your Corporate Headquarters
If there is "Comm"/"speak to" task, then there should be a "mission giver" to talk to at the SY.