Scenting is the simplest method besides just trying one (but I assume since you say he is picky that you've tried to just feed a rat as-is before). Rub the rat on the mouse or thaw one of each together in a baggie so the mouse smell rubs off on the rat then offer it after heating. Blow drier works better than hot/warm water to heat it up to life-like temperatures for this since it doesn't wash the smell away.
If round 1 or 2 fails, you can try slower and feed a rat-scented mouse a few times to get the smell more familiar and then feed the mouse-scented rat.
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