Remember my last?

Let me start 의해 saying I don't KNOW.

I personally believe it'd be something along the lines of 'remember the last things I said to you' which presumably would be something to do with how important Harry is.

At a guess.

I think he explained her that to have her sisters sacrifice a meaning, Harry would have to stay with her moms family (meaning her) so he can be protected 의해 Voldemort. The things he said to Harry at the end.

The 'last' was the letter he left for her with Harry, saying if she accepted him, and took him in, she would be offering him protection from Volde. He asked her ot care for Harry, and treat him as her own, and always allow his 집 to be with her.

That's why he said what he did OotP and HBP.