A federal appeals court on Friday affirmed a finding that Tesla illegally fired an employee involved in union organizing, and that the company’s chief executive, Elon Musk, had illegally threatened workers’ stock options if they chose to unionize.

The opinion, by three judges on the U.S. Court of Appeals for the Fifth Circuit, allows the National Labor Relations Board to enforce a 2021 order requiring Tesla to reinstate, with back pay, the employee, Richard Ortiz, and Mr. Musk to delete a Twitter post suggesting workers could lose stock options if they unionize.

“I look forward to returning to work at Tesla and working with my co-workers to finish the job of forming a union,” Mr. Ortiz said in a statement.

Tesla did not immediately respond to a request seeking comment on the ruling.

The finding comes as other companies run by Mr. Musk have had workers raise concerns about labor law violations. Last year, eight former employees at SpaceX, the rocket manufacturer led by Mr. Musk, filed charges of unfair labor practices, saying the company had retaliated against them for helping to write a letter asking for better enforcement of its stated policies on sexual harassment. The cases are pending.

In February, Tesla fired at least 18 employees as a result of a union organizing campaign at a plant in Buffalo. The union seeking to represent the workers called the firings retaliatory and filed charges with the labor board. Tesla said in a statement that the firings were a result of a semiannual performance review and that the termination decisions had been made before the union campaign went public.

The case at issue on Friday dates to 2017. At the time, Mr. Ortiz was known to be involved in an effort to unionize the company’s plant in Fremont, Calif., which included distributing union material and pressing for pro-union legislation, when he posted screenshots of his co-workers who were anti-union on a private Facebook page.

When a company investigator asked Mr. Ortiz where the screenshots came from, Mr. Ortiz said he didn’t remember, though a colleague had sent him the pictures after getting them from an internal human resources site. Mr. Ortiz later admitted that his response was a lie, and the company claimed it fired him over the false statement.

The labor board concluded that Mr. Ortiz had been fired because he was engaged in union activity, not because he had lied. The circuit court agreed that “substantial evidence” pointed to the conclusion that “union animus motivated the complaint, the investigation and the decision to terminate Ortiz.”

Mr. Musk’s post from May 2018 about stock options said there was nothing stopping Tesla’s employees at the plant from voting for a union, adding, “But why pay union dues & give up stock options for nothing?”

Tesla argued that the statement was a straightforward prediction based on Mr. Musk’s understanding that other members of the United Automobile Workers union did not receive stock options, and that his benign intent became clear in subsequent posts in the same thread.

But the labor board concluded that the post would have been interpreted by employees as a threat to eliminate their stock options if they chose to unionize and ordered Mr. Musk to delete it. The circuit court agreed and said the board could enforce its order.