Since there is no direct source quoted, I’ll remain skeptical. There’s loads of Hitler legends running around the Internet.
I did a search on Hitler’s quotations about firearms and came up with this on Snopes (although I don’t always believe Snopes):
Whether this quote could be considered “true” in the sense that it compactly paraphrases an idea that Hitler once expressed depends upon how one interprets its meaning. The book Hitler’s Table Talk, 1941-1944: Secret Conversations records Hitler as having said the following sometime between February and September 1942:
The most foolish mistake we could possibly make would be to allow the subject races to possess arms. History shows that all conquerors who have allowed their subject races to carry arms have prepared their own downfall by so doing. Indeed, I would go so far as to say that the supply of arms to the underdogs is a sine qua non for the overthrow of any sovereignty. So let’s not have any native militia or native police.
If the term “conquering a nation” in the original quote is interpreted to mean that establishing and maintaining oneself as the autocratic head of a country (as Hitler did in Germany) requires disarming the civilian population, then the Table Talk passage cited above doesn’t really fit — Hitler was speaking of the need to disarm non-Aryans in the parts of Russia that had been occupied by German forces in the midst of a war, not of stripping all Germans of their guns. (And it’s unlikely that Hitler would have expressed such a concept in this context, as the 1938 German Weapons Act passed during Hitler’s rule actually loosened gun ownership rules for non-Jewish Germans.) If the term “conquering a nation” is interpreted to mean that the forcible overthrow and takeover of another country’s government and territory necessitates the disbanding and disarming of even local security forces, then the passage cited above might be considered as expressing the same idea as the original quote.