"I already put that envelope in the mailbox."
Interesting observation. Since the topic establshes the perameters of the comment, putting もうafter the topic makes it part of the comment, expressing what has been done to the envelope. Putting it before the topic would make it part of the broader utterance, expressing what the subject ("I") has already done. Physically the same thing happens in either case and the difference between the utterances is so subtle that speakers may not notice it. Since the topic-comment structure of Japanese is what makes the distinction possible, it is very hard to reflect it in English except by intonation and positioning of adverbs.
The reason for putting it before ポスト is to encapsulate the entire action involving the envelope (は topic), it's more natural to ask/say what has already happened in it's entirety, i.e. 'already put in' by itself isn't an acceptable response, as it would automatically entail the question 'in what?' to follow. To avoid this, you put もう where it serves as a qualifier to whatever level of a process you want to indicate has been done. Hope my rambling made some sense.
Duo's sentence is a statement about the envelop. It would answer the question, "What did you do with the envelop?" The presumptive topic of your sentence would be the speaker and there would be some contextual reason for saying what the speaker did as contrasted with what someone or anyone else did.
The sentence with "wo" instead of "wa" is grammatical but it implies an understood topic. That is, the sentence with "wa" tells you what happened to the envelop (which is the topic) while the sentence with "wo" is a comment implying that mailing the envelop has to do with a broader context (like things I've done today).