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Apparently the cat had to sit still long enough for the fly to lay the larva. This probably happened when she was watching a rabbit hole to see if any babies would exit. She was until a couple of months ago an indoor cat so she's not well prepared to deal with the wild, especially the little critters crawling and flying around our backyard.
Yes. According to Wikipedia it has many common names. Botfly is what my local veterinarian called it when she removed it from the shoulder of my cat.