I have a FAA Private VFR SE license based on my foreign license, and added IFR in my home country; how to upgrade the FAA license?
I assume that your FAA private license was issued under 14 CFR 61.75, and that section also includes the requirements for adding instrument privileges:


  (d) Instrument ratings issued. A person who holds an instrument rating
  on the foreign pilot license issued by a contracting State to the
  Convention on International Civil Aviation may be issued an instrument
  rating on a U.S. pilot certificate provided:
  
  (1) The person's foreign pilot license authorizes instrument
  privileges;
  
  (2) Within 24 months preceding the month in which the person applies
  for the instrument rating, the person passes the appropriate knowledge
  test; and
  
  (3) The person is able to read, speak, write, and understand the
  English language. If the applicant is unable to meet one of these
  requirements due to medical reasons, then the Administrator may place
  such operating limitations on that applicant's pilot certificate as
  are necessary for the safe operation of the aircraft.


The "appropriate knowledge test" in this case is the Instrument Rating - Foreign Pilot test, it's described here with a few sample questions. Some more information is here, including the point that you don't need any prior authorization to take the test:


  • Requires NO instructor endorsement or other form of written
  authorization.


I'm not sure about the exact process involved (I guess you just do the test and send the certificate to the FAA) but the FSDO that validated your foreign license for VFR should be able to give you all the details.