Are you sure? Would Zanz have copies Just in case?
In 1964 Coast Hospital in Mombasa was within the Coast Province of the Republic of Kenya. If someone wanted a certified record of a birth in that hospital in 1961, he would go to the bureaucrat responsible in 1964 for Mombasa and its hospitals. Where the records for Mombasa from the time when it was still NOMINALLY under Zanzibar (but already effectively within the British colonial administration were kept in 1964 doesn’t matter. The bureaucrat would go to wherever those books were kept and look up that birth and fill out the certificate. But since the book is given a number and no further identification, the original book recording births in Mombasa (Zanzibar) in 1961 was known to the registrar of births in the Coast Province of Kenya in 1964—the records of the British colonial bureaucracy were simply being continued, probably in many cases by the same bureaucrats who ran those offices before Kenya’s independence in the preceding fall.
None of this means the document is not a fake. A forger would research the bureaucratic structure of the period from 1961-1964 and gotten the names of the officials and found out how records were kept and filled in the blank form with that information.
That’s why Freepers can’t decide this question on these threads. Only someone with this document in hand doing forensic work on it can do that.
It may well be a fake. It could be an effort to divert attention from Obamacare etc.