Prince Weimin was a prince with a different surname and was sworn enemies with Prince Ying. Although his power was not as great as Prince Ying's, and his fief was not as large as Prince Ying's, he was the most ambitious and disloyal of all the princes with fiefs.
As long as he sent someone to kill Princess Jin, he would be able to stir up internal strife in the royal family and reap the benefits. Even if Prince Weimin didn't know who wrote this letter, what their intentions were, or whether they were using him, Prince Weimin would still send his trusted aides, who would never betray him, to Xinyuan to confirm if the letter was real or fake. If he really saw Princess Jin, he would definitely kill her without hesitation.
