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I was thinking just fill it by opening the existing reservoir lid just enough to pop a tube in, fill a bit of tupperware with the water, pop the other end of the tube in the water and lift it above the coffee machine to siphon it in.
Though after thinking about it, if I were in your position I'd probably end up getting a tupperware container, drilling a hole in it to fit a little tap (like these: https://www.amazon.co.uk/dp/B0746CFNNP). Then run a hose from the tap, through a hole in the bottom of the cupboard, into the reservoir.
Do you mean don't use the supplied reservoir in the back and put pipes into something else?