
I am not sure if this kind of reported speech implies that the father was a teacher at the time of the saying, but isn't a teacher anymore, or that he has been and still is a teacher, or that both are possible.

Both are possible. The use of "était" doesn't imply that the father is no more a teacher, nor does it imply that he's still a teacher. He was just a teacher at the time of the saying. There's no information about what he is today.
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