I would first calculate the ...

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I would first calculate the correlation between both stations for monthly data, which you have and you can calculate for station A. If correlation is trustworthy, then I would use a double mass curve or use a model to infer daily data for station B.
If you don't get a good correlation, I would probably search for other stations or you will have to use station A alone.

Always keep in mind that the interpolated data, by any method, it will not be very useful for predicting extreme values. So, it will depend on what you want to do with the data.