"Please allow us to send you a small gift of short shorts to help you through this difficult time," Musk wrote, invoking a jab he has used with Tesla short sellers, or investors who bet against a company's stock performance.
Musk, who is known for publicly sparring with Tesla naysayers, previously sent Einhorn a box containing several pairs of short shorts, to which Einhorn responded with a sarcastic thank you via Twitter.
Einhorn's Greenlight Capital has long had a large short position in Tesla, meaning it loses money when Tesla's stock performs well.
When Tesla posted a surprise profit on October 23, sending its share price up 30%, Greenlight took a significant hit.
One lawsuit filed by Tesla shareholders alleges Musk engineered the purchase of SolarCity, in which he was the majority shareholder, as a a bailout of the troubled solar panel company.