What is the process to get a simulator FAA certified for IFR training?
The FAA Advisory Circular 61-136 contains the guidance for Aviation Training Devices, including the BATD's.   

The AC states that as long as the system has been FAA approved by the manufacturer (and in your case you say that it "meets the FAA requirements"), that no specific approval is required for training conducted under 14 CFR 61.  For use under 14 CFR 141 however, you would need specific FAA approval (see below).

14 CFR 61 Approval

You must simply follow the conditions specified in the AC:


  5. APPROVAL OF BATD FOR USE UNDER PART 61. To be approved for use for pilot   training and certification under part 61, a BATD should:  
  
  a. Be capable of providing procedural training in all elements for
  which it is to be used.  Those elements should be specified in an
  acceptable training curriculum or as specifically  authorized by the
  FAA and meet the description and suggested criteria outlined in this
  appendix.
  
  b. Have the following documents available for inspection by the
  student and instructor: 
  
  
  The list of ATD components as required by paragraph 3c, 
  A copy of AFS-800’s letter of approval and authorized use of the ATD, and 
  A copy of the QAG for the ATD being used.   
  
  
  c. Successfully pass the start-up self-test described in paragraph
  8c(2). If the device is being used in a course of training for a pilot
  certificate or rating, a person authorized by the FAA to provide
  ground or flight instruction should observe this test. After the ATD
  self-test is complete, no other software of any kind may be started on
  the computer running the ATD software.   
  
  d. Remain in the approved configuration during the training session.
  Authorized ATD  instruction may not proceed after a malfunction of the
  ATD system has occurred. The operator  must correct the ATD
  malfunction and repeat the start-up test described in paragraph c of
  this section before resuming authorized instruction. In addition, a
  BATD may be used in a training curriculum that provides for:  
  
  
  A similar scope and content of a syllabus that is used under part 141; 
  Instructional materials for flight events; 
  A means of showing progress, such as an outline of stage (phase) checks and criterion  levels of performance; and 
  The authorized use as approved in the AFS-800 letter of approval.
  


14 CFR 141 Approval

141 Approval is almost the same, but must be approved by the school's POI (principle operations inspector):


  6. APPROVAL OF BATD FOR USE UNDER PART 141. Local FSDO may approve  BATDs as part of an overall part 141 curriculum approval and
  certification process. Pilot schools that want to use a BATD as part
  of their training curriculum must notify their principal operations
  inspector (POI). The POI is responsible for approving how the BATD is
  to be used in the certificate holder’s part 141 curriculum. To be
  approved for use under part 141, a BATD should:  
  
  a. Be capable of providing training in all elements in which it will
  be used, as specified in the syllabus, and meet the description and
  suggested criteria outlined in this appendix.     b. Have the
  following documents available for inspection by the student and
  instructor:   
  
  
  The list of ATD components required in paragraph 3c, 
  A copy of AFS-800’s letter of approval and authorized use of the ATD, and 
  A copy of the QAG for the ATD being used.  
  
  
  c. Successfully pass the start-up self-test described in paragraph 8c
  of this appendix. A  person authorized by the FAA to provide ground or
  flight instruction should observe this test. After the ATD self-test
  is complete, no other software of any kind may be started on the
  computer running the ATD software.   
  
  d. Remain in the approved configuration during the training session.
  Authorized ATD  instruction may not proceed after a malfunction of the
  ATD system has occurred. The operator  must correct the ATD
  malfunction and repeat the start-up test described in paragraph c of
  this section before resuming authorized instruction.  
  
  e. Be used in an integrated ground and flight training curriculum
  which provides for:  
  
  
  The scope and content of a curriculum in compliance with part 141, 
  The authorized use as approved in the AFS-800 letter of approval, 
  Instructional materials for flight events, and 
  An outline of stage (phase) checks and criterion levels of performance.