if I transfer ebm from refrigerator freezer to deep freezer, does it last three months or six months?

Ideally 3 months only as your 1st point you had put into the normal freezer. Only if the 1st point you put into the deep freezer, then you can keep it for up to 6 months. I would think as long as they are not towards the end of the 3-4 month time frame, they would still last at least 6 months in deep freeze. There is a difference between the frozen milk and freshly expressed, but both are still good, with the fresh being a tad bit better, due to components being broke down. My suggestion is to freeze what you pumped immediately into the deep freezer.

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3 months, shorter lifespan because it wasn't in deep freeze from the start.

Just 3 months, I would say.