I have already asked a similar question at https://math.stackexchange.com/questions/470704/can-a-brouwerian-lattice-be-extended-into-a-boolean-algebra but have received no answer. Sorry, I ask a similar question second time, as it is very important for my research. Is it true that every Brouwerian lattice (=locale =frame) can be order-embedded into a Boolean lattice? If yes, can we warrant that this embedding preserves joins and finite meets?