The e-mail that flooded Billpoint’s offices one day last October carried welcome news: The company’s top rival in the person-to-person Internet payments business, PayPal, had begun collecting fees from longtime users, and they were looking to defect.

It was a day of “great delight” in Billpoint’s San Jose, Calif., offices, said Janet S. Crane, chief executive officer of the company, which is 65%-owned by eBay, the Web auctioneer, and 35% by Wells Fargo & Co., Ms. Crane’s former employer.

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