Hello
I am not familiar with these terms, I had to consult a person who is very close to Greek Orthodox priests and monasteries. This is his answer :
You begin the letter with the salutation:
Άγιε Καθηγούμενε (if addressing a male) or
Αγία Καθηγουμένη (for female)
You can follow with the name of the recipient, but this would make it less formal.
If the person has a university degree, you can precede the above with the words : Οσιολογιότατε/Οσιολογιοτάτη
If you do not know if they have a university degree, you can still use it out of respect and to be on the safe side:
Οσιολογιότατε Άγιε Καθηγούμενε (male) or
Οσιολογιοτάτη Αγία Καθηγουμένη (female)
A formal way to end the letter is : Ασπάζομαι την Δεξιάν σας
A less formal way to end it is : Εύχεσθε
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.