Q. I once heard from Rav Shlomo Miller shlit”a that one may not append the term a”h to the name of the deceased if the deceased was not observant, because a”h means that the Divine Presence hovers over the grave of such a person and it would not do so over a non-observant person.

What alternative abbreviation, if any, may be used, in English and in Hebrew, especially if one wishes to avoid unpleasant confrontation?

A. Horav Shlomo Miller’s Shlit”a opinion is that if the deceased indeed qualifies as non-observant by conviction and belief and not only by accident such as a “tinok shenisba” (a “captured child” who was denied proper Torah education), the term “Tehey menuchoso b’shalom” which is more a plea and a blessing would be appropriate. The expression “alav hashalom” as you mention, is a statement connoting that Shechina hovers over him, which probably may not be true.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a