WASHINGTON — Rudolph W. Giuliani, President Trump’s personal lawyer, signaled this month that he planned to open a new front in his attacks against former Vice President Joseph R. Biden Jr. — work done by Mr. Biden’s son Hunter Biden for a wealthy Romanian business executive facing corruption charges.

But there’s a problem with that strategy: Mr. Giuliani participated in an effort that would have helped the same executive, and was in fact recruited to do so by Louis J. Freeh, a former F.B.I. director who had been brought onto the matter by Hunter Biden.

In effect, Mr. Giuliani and Hunter Biden were on the same team, if not at the same time. And their work to help the business executive, along with that of Mr. Freeh, stood in contrast to efforts by the United States, including Vice President Biden while he was in office, to encourage anti-corruption efforts in Romania.

The dynamic in Romania underscores how Mr. Giuliani has done a brisk international business with clients who sometimes seem to be seeking to capitalize on his connections to Mr. Trump even as he has accused Hunter Biden of seeking to capitalize on his father’s name while doing business in other countries. And the disclosure of the connection between his role in Romania and Mr. Biden’s comes at a time when Mr. Giuliani, the former New York mayor, is under investigation by federal prosecutors in New York for possible violations of foreign lobbying laws.