Yes.. The certificate number will not change. The flight instructor certificate includes
CFI at the end of your number.
§61.5 Certificates and ratings issued under this part.
(a) The following certificates are issued under this part to an applicant who satisfactorily accomplishes the training and certification requirements for the certificate sought:
(1) Pilot certificates
(2) Flight instructor certificates.
(3) Ground instructor certificates.
Part 63 provides guidances on flight engineer and flight navigator certificates.
Part 65 provides guidance for ATC tower personnel, mechanics, repairman, parachute riggers, and dispatcher certificates.