For example, A gives a gift to B.
A: here’s my gift for you.
B: I’ve been waiting for your gift.
Should B call the gift ”my gift” or ”A’s gift”?
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my possessive determiner 1 Belonging to or associated with the speaker. ‘my name is John’ ‘my friend’ - ODO
The problem is that "my" can denote mere association with the speaker. So "my gift" can be the gift that "I" give or the gift that "I" receive. This ambiguity also holds when you change "my" to "A's" or "your" etc.
When you pare down the sentence to something like "my gift" or "A's gift", you lose the contextual clues that tell you which version it is.
The way around this is to include enough context that the 'direction of giving' is clear. E.g. "A's gift to B". However, if the context already makes it clear, the short version can stand. Consider: