Vice President Kamala Harris is trying to escape the shadow of President Biden, but her campaign emails still say “joebiden.com.”

The email domain address is among a slew of valuable assets transferred from the Biden campaign to the Harris campaign last month. Other assets include leases for field offices, campaign staff, and, most importantly, hundreds of millions of dollars in contributions.

The handoff of those assets from President Biden to Ms. Harris enters a murky area unresolved by either the Federal Election Commission or the judicial system.

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Bradley E. Smith, who served as commissioner, vice chairman, and chairman of the FEC, said those are valuable assets that must be accounted for.

“No one has ruled on this in the past. I think the better interpretation is that the transfer is not legal, but it’s not like the Democrats don’t have a leg to stand on,” he said.

Since Ms. Harris took over the Biden campaign, it is largely the same, but with a different name at the top. She has retained Mr. Biden’s campaign chair and campaign manager, assumed control of the campaign’s headquarters in Wilmington, Delaware, and kept the “@joebiden” domain name.

Ms. Harris, who won the Democratic presidential nomination Friday in an online vote by party delegates, also claimed ownership of the roughly $96 million held in accounts controlled by the Biden campaign committee. She also gets access to roughly $240 million in cash on hand split across the campaign, the Democratic National Committee, state Democratic Parties and various fundraising committees.

Democratic voters are left to ponder how she got the nomination without winning a single primary vote while Biden donors wake up to their money sitting in Ms. Harris’ coffers.

Ms. Harris is bringing in a deluge of new contributions in her own right.

As of Thursday, her campaign bank account has ballooned to $377 million.

Former President Donald Trump’s campaign filed a complaint with the Federal Election Commission alleging the transfer of those funds violated campaign finance laws. The complaint was filed against Mr. Biden, Ms. Harris, the Biden campaign and campaign treasurer Keanna Spencer.

“Kamala Harris is seeking to perpetrate a $91.5 million heist of Joe Biden’s leftover campaign cash — a brazen money grab that would constitute the single largest excessive contribution and biggest violation in the history of the Federal Election Campaign Act of 1971,” the Trump campaign wrote in the complaint.

The core of Mr. Trump’s argument is that Ms. Harris simply replaced Mr. Biden’s name with her own rather than filing her own Statement of Candidacy. The complaint to the FEC contends that no provision in federal campaign law allows for the repurposing of one candidate’s campaign for the use of another candidate.

In a statement, a Harris campaign spokesperson dismissed the FEC complaint as meritless.

“Republicans may be jealous that Democrats are energized to defeat Donald Trump and his MAGA allies, but baseless claims — like the ones they’ve made for years to try to suppress votes and steal elections — will only distract them while we sign up volunteers, talk to voters and win this election,” said spokesperson Charles Kretchmer Lutvak.

The transfer of money and assets remains unprecedented in U.S. history. Federal law states that any “campaign depository” for a presidential candidate “shall be the campaign depository for that political party’s candidate for the office of the vice president.”

Some argue that means Ms. Harris is entitled to Mr. Biden’s cash because she has been jointly listed in his campaign’s FEC filings since she became his running mate in 2020.

But Mr. Smith said that under the law, the Biden-Harris team must be formally nominated by their party before the money could be shifted. Under that interpretation, Mr. Biden wouldn’t be able to transfer the donations and assets until after the Democratic National Convention later this month.

“You can’t say that because Harris was nominated to be Biden’s vice president in 2020, that she is automatically on this committee,” Mr. Smith said. “Biden could drop her from the ticket, she could challenge Biden in a primary and decide to quit being vice president and run for senate in California. In all of those scenarios, she’d have to start her own campaign committee.”

“She doesn’t get to piggyback off Biden indefinitely,” he said.

Trevor Potter, a Republican former chairman of the Federal Election Commission, disagreed. He said that because Ms. Harris was part of Mr. Biden’s election committee, she was entitled to his cash and campaign assets.

“Specifically, because Biden and Harris share a campaign committee, the vice president and her running mate can continue using the campaign’s existing funds for the general election if she is on the Democratic ticket as either the presidential or vice-presidential nominee,” he said.

Daniel I. Wiener, director of the Brennan Center’s Elections & Government Program, authored an op-ed saying he interprets the law to favor Ms. Harris, but he said there was some room for legal argument on whether that is correct.

He also said the same law that allows Mr. Biden to transfer his assets to Ms. Harris hamstrings her ability to solicit funds. Under the FEC rules, two candidates running under one ticket are subject to a single set of contribution limits. That means if a wealthy donor maxed out their legal contribution to the Biden campaign, the Harris campaign cannot go back and solicit more money from them. If the Harris campaign were considered separate from Mr. Biden’s campaign, she would be able to ask these donors for more money.

Regardless of how the complaint shakes out, it’s likely to have little impact on the election. The FEC is notoriously slow when it comes to resolving disputes.

Under the FEC’s statute, it takes 60 days before its commissioners can act on a complaint, meaning the agency won’t even touch the case until sometime in mid-October.

And complex cases such as this usually take anywhere from one to five years to resolve, meaning voters would be lucky to have an answer before the 2028 election campaign.

The Trump campaign could go to a federal court and ask a judge to issue an injunction blocking Ms. Harris from receiving the funds, but Mr. Smith said that gambit would likely go nowhere.

“What federal judge is going to issue an injunction so close to the election?” He said. “No judge is going to do that.”