Srila Prabhupada gave Diksa-mantra through Tape

Srila Prabhupada had disciples hear the TAPE of him giving Gayatri Mantra at brahmana initiation. 

Srila Prabhupada's Letter to Gaura Hari, September 24, 1971:

"At your recommendation I have gladly consented to accept Guy as my duly initiated disciple. His letter and beads are enclosed herewith. Also enclosed are three sacred threads duly chanted by me as well as four papers with Gayatri mantra for the four devotees you have recommended for second initiation. You should secure the tape of me reciting Gayatri mantra from Makhanlal in Seattle. Let each devotee hear the tape privately, one at a time, and through the right ear. They should have the paper in front of them and hear and repeat each word. Beforehand you can show them how to count on the fingers, and beforehand hold a fire yajna and get the threads on the boys' bodies."

3) Srila Prabhupada had the WIFE of one disciple read Gayatri mantra to a devotee. 

Srila Prabhupada's Letter to Vaikunthanatha, Sardia, April 4, 1971:

"Even though you have had no gayatri mantra, still you are more than brahmana. I am enclosing herewith your sacred thread, duly chanted on by me. Gayatri mantra is as follows:

[TAKEN OUT]

Ask your wife to chant this mantra and you hear it and if possible hold a fire ceremony as you have seen during your marriage and get this sacred thread on your body. Saradia, or any twice-initiated devotee, may perform the ceremony.

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THE GURU HAS TO BE PHYSICALLY PRESENT IS A MYTH.

Physical presence is immaterial. Presence of the transcendental sound
received from the Spiritual Master should be the guidance of life.
That will make our spiritual life successful.

(SP Letter to Brahmananda and other students, 19/1/67)

So we should associate by vibration, and not by the physical
presence. That is real association.
(SP Lectures SB, 68/08/18)

The vibrational conception is eternal.(SP in Elevation to Krishna Consciousness,(BBT 1973), Page 57)

I shall remain your personal guidance, physically present or not
physically present.(SP Room Conversation, Vrindavan, 14/7/77)

I am always with you. Never mind if I am physically absent.
(SP Letter to Jayananda, 16/9/67)

So although a physical body is not present, the vibration should be
accepted as the presence of the Spiritual Master, vibration. What we
have heard from the Spiritual Master, that is living.
(SP General lectures, 69/01/13)

and for more quotes :

http://prabhupadanugas.blogspot.com/2011/11/shrila-prabhupadas-quotes-on-vani-and.html