As a creative writing assignment, the answer to this question is really completely up to you. Likely, your teacher is looking for your insight and creativity, so I encourage you to think about this for yourself and include only your own opinions.
From my perspective, the same story told through Oskar's mother's eyes would be a far different story. First, it would lack all the delightfully innocent and precocious humor that Oskar so unwillingly includes. Also, if you remember, Oskar's mother was experiencing a very personal grief that didn't often include Oskar. He needed her, but she was emotionally unavailable. I imagine her story would be riddled with pain, confusion, and a maternal sense of guilt. It is likely that she is aware of her son's need for her, but is simply unable to provide for him emotionally. I wonder too, how much of the mystery of Oskar's story would be expelled by revealing what his mother actually already knows.
Finally, I wonder how much more complex of a character would be revealed in her, if she was telling the story herself. From Oskar's perspective, his mother seems self-absorbed, a little flighty, and though good-intentioned, she seems to constantly fall short. It would be interesting to see the psychology behind her grief and have the opportunity to empathize with her more.
As I said, it would likely be a very different and certainly not a whimsical or happy story.