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Female boesemani do have some dark markings when breeding but I don't recall them having black lines like that. Having said that, I don't know of any rainbowfish that have black lines running vertically up and down the body.
You need a picture on the back of the tank and some Duckweed on the surface for them to eat.
Give the female a few more months to grow and see how she looks then.
Can you check the size of your fish?
The fish does not look like it is four and a half inches long. My guess is the fish is about 2 inches and is a young male.
Melanotaenia praecox (neon blue rainbows) only grow to about 2 inches maximum and the boesemani is a similar size the male M. praecox.
Male rainbowfish produce a dorsal blaze, which is the gold, white or pink stripe that flashes on and off when they breed. This stripe is located on top of the head and runs from the start of the first dorsal fin and goes down to the nose. Female rainbowfish do not produce a dorsal blaze.
My bad, I'm terrible at estimating. Used a ruler and she's more like 3 inches.
Even if it is a male, I'm still intrigued by the black vertical stripes.