What did Conan, a famous detective, write on the short message?

What the landlord asked was the words in the Japanese version of "Invitation Letter with Secret Code".

The last message is the password.

The hiragana in front of it is written words, そんけなぉとぃことわけれてよぃかつ.

It wasn't fun at first.

The last sentence is ケムシとィモムシ.

ケムシ means caterpillar, ィモムシ means caterpillar. The original meaning of this sentence is caterpillar and cabbage caterpillar. However, in Japanese, the following ムシ is homophonic with ignoring, that is, ignoring ケ (け) and ィ (ぃ) above.

So the text becomes

そんな おとことわれて よかったね

It means "such a man should break up with him."

Because Miss Kaoru knows "Civet Cat Code", that is, civet cat is たぬき (raccoon) in Japanese, and the following ぬき (き) means to be removed, which means to be removed together. This principle is exactly the same as the previous "Caterpillar and Caterpillar", so Conan believes she can understand it.