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I know that when giving something, you can say 父に傘を貸してあげました - there's only one word for when giving. But when receiving something, it's either 〜もらいました or 〜くれました.
It's my understanding that, when the subject is myself, we use 〜もらいました, and when the subject is the other person, it's 〜くれました. Is this correct, and are there other considerations that I should be aware of?