Is it permissible to use the phrase "تهديكم أطيب تحياتها" (sends you its best greetings/salutations) in official letters, given a previous fatwa prohibiting the use of the word "تحيات" (greetings/salutations)?

It is best for a Muslim to greet his brother with the legitimate greeting, "As-salamu alaykum" (Peace be upon you) or "As-salamu alaykum wa rahmatullahi wa barakatuh" (Peace be upon you, and the mercy of Allah and His blessings), because it includes respect, supplication, honor, and security. This is the greeting that Allah taught Adam, peace be upon him. There is no harm in saying "My greetings" or similar phrases, though it is preferable to adhere to the legitimate expressions.