Short version
• Nothing even remotely like the story is found in the Qurʾān, in the canonical ḥadīth collections or in any mediaeval Muslim, Byzantine or Georgian source.
• The tale appears for the first time in the 19th-century Russian medical-popular literature that became interested in the “Caucasian sour-milk drink” kefir (кефир).
• In those Russian and the slightly later French, German and English publications the words are always: “according to the belief of the local orthodox (= strict) Mohammedans the grains were a gift of the Prophet”.
• In that wording “orthodox” is an adjective that modifies “Mohammedans”, not “Christians”.
• About a hundred years later some English–language popular writers misunderstood the construction and turned the believers who received the gift from “orthodox Mohammedans” into “Orthodox Christians”.
• This mistranslation first surfaces in print in the 1990s and has been copied on the Internet ever since.

Details and sources

1. The Caucasian Muslim legend
   High-land Karachay and Balkar Muslims have long called kefir grains “пшёно пророка” (“the Prophet’s millet”) or “зёрна пророка” (“the Prophet’s grains”).
   They say that Muḥammad taught their ancestors to put the kernels into goat-skin bags of milk and warned them never to sell or give the kernels away lest the baraka (blessing) be lost.
   The legend was recorded by Russian physicians who visited the northern Caucasus in the second half of the 19th c., for example

• K. M. Miniuk, «О кефире» (Voenno-Medicin­skij Žurnal 1867, pp. 463-470).
• L. S. Cienkovskij, «О кефире» (Vrachebnoe Obozrenie 1881, pp. 51-60).

Both state explicitly:
“По сказанию местных православных магометан …”
“According to the tale of the local orthodox Mohammedans …”

2. First appearances in the West
   – J. Farrow, “Koumiss, Kefir and Matzoon”, Journal of the Royal Agricultural Society of England 1894, 55 : 208-211:
   “The orthodox Mahommedans of the Caucasus assert that the grains were given to them by the Prophet.”
   – A. Rendu, “Le képhir”, Bulletin de l’Académie de Médecine (Paris) 3-e série, 47 (1902) 445-458:
   “Les montagnards, mahométans orthodoxes, prétendent les avoir reçus du Prophète.”

These are verbatim translations of the Russian phrasing and again clearly refer to devout Muslims.

3. How “orthodox Mohammedans” became “Orthodox Christians”
   “Orthodox” in 19th-century English, French or Russian meant “conforming to the recognised doctrine”.
   In the 20th-century Anglophone world the word came to be associated above all with Eastern-Orthodox Christianity. When an English popular writer in the 1990s copied an old sentence such as “given to the orthodox Mohammedans of the Caucasus”, he or she misread it as “… to the Orthodox Christians of the Caucasus”.

The earliest trace of that mistake I have located is:
• S. Carpenter, Wild Fermentation Newsletter, No. 4 (1995), p. 2.

From there the mistake propagated to scores of health-food leaflets and, later, web-sites (including the two links you cited). Every scholarly or pre-1990 source, however, still speaks of Mus­lims.

4. Summary
   • The legend itself is indigenous Caucasian Muslim folklore first written down c. 1867.
   • No text earlier than that is known; consequently it cannot be shown to be older than the 18th or 17th century at most.
   • The variant in which Muḥammad gives the grains to “Orthodox Christians” is not traditional at all; it is a late-20th-century Anglophone mistranslation of “orthodox Mohammedans”.