Is the second party, who received money from their partner without it being specified whether it was a loan or not, entitled to consider this money lawful for themselves and refuse to return it, claiming that it was profit from a suspicious transaction in which both parties were defrauded?

The question is vague concerning the ambiguity and the type of unlawful money.

If the money results from unlawful gain such as usurious interest and gambling, then it does not belong to anyone, and it should be spent for the general welfare and benefit of Muslims, such as orphanages and Qur'an memorization centers. Whoever acquired it must spend it in these channels, and the one from whom it was taken has no right to claim it for personal ownership, but rather to ensure it is spent in its lawful channel. And he is liable for it if he neglects its safekeeping, in which case the responsibility for what was spent falls back on the original acquirer.

However, if the money was taken by usurpation or theft, it must be returned to its owner. If it is not returned, then its liability rests upon the initial usurper, based on the Hadith (definition): "The hand is liable for what it takes until it returns it."