1. A Minor point but, it is not a 87-10 form... it is a 8710-1 form.
2. An expired CFI can be re-instated during a 135 aircraft check ride with the prior agreement of the Inspector or Approved DPE. As long as the activities of the flight meet the requirements for CFI renewal, it can be done.
3. The below reference is from the Air Carrer Inspectors Handbook. A renewal can be based on: If "the Airman is in a position to evulate pilots". In a two pilot aircraft the Captain can evulate the First Officer for upgrade potential (depending on the companies manual prodedures).
Hope this helps.
JAFI
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FAA Order 8400.10
VOLUME 5. AIRMAN CERTIFICATION AND DESIGNATED EXAMINERS
CHAPTER 9. SELECTED PRACTICES
SECTION 6. RENEWAL OF FLIGHT INSTRUCTOR CERTIFICATES
765. GENERAL. This section contains guidance and
information for inspectors concerning the renewal of current
flight instructor certificates for pilots conducting
operations under Part 121 and Part 135.
Operations Inspector’s Handbook.
C. Other Activities Regularly Involving the Evaluation of
Pilots. An inspector may renew the flight instructor
certificate of an airman involved in any activities regularly
involving the evaluation of pilots; such activities might
include simulator-only instruction. In some cases, it may
be necessary for the applicants to demonstrate knowledge
of current pilot training and certification requirements and
standards by passing an oral test administered by the
inspector.