Recently, my brother and one of his collegues were enjoying an off-color joke at work when yet another collegue approached and asked what was so funny. My brother and the other collegue proceded to tell the joke to the young lady who had approached and asked to participate in the conversation. Upon understanding the punchline, the young lady enjoyed a good laugh and the three of them went back to work. Four days later, the young lady messaged my brother that she wanted to work with him that weekend, so he could train her in some areas in which she felt he excelled. My brother was busy and did not respond to this request. Consequently, he arrived at work the next day to find out that he and his collegue were facing a 5 day paid suspension followed by a week unpaid suspension for "hostile work environment" sexual harassment since the young lady had reported to supervisors (a week later) that she was offended by this joke. My question is this...
Since the young lady asked specifically to work with and train with my brother days after this allegedly "offended her" and "made her uncomfortable", couldn't this show that she really wasn't offended at all by a joke but perhaps an unanswered message? Furthemore, since my brother and the other collegue did not initiate the conversation but the young lady asked to be involved, does this change things at all? Though I understand that the workplace is not an appropriate forum for off-color jokes (regardless of how elementary they are in nature) I wonder if this suspension is a bit unfair considering all the circumstances. Please advise.

While a suspension might or might not be unfair, this was not "wrongful" in the legal sense of the word. I don't mean this as bluntly as it will sound, but the employer is not required to be fair, only to be legal, and suspending your brother was not illegal.

When a complaint of SH is made, the employer is required by law to take whatever action is required to make the harassing behavior stop. As you point out, off color jokes are inappropriate in the workplace whether anyone is offended or not. A suspension for inappropriate conversation in the workplace would not be unfair.