"I had congratulated Nitishji on February 7, 2015. Let me congratulate him again today," Banerjee, Trinamool Congress supremo, who is now in Dhaka on a three-day visit to Bangladesh, tweeted.
Kumar, who met Governor K N Tripathi during the day, was invited to take oath on Sunday (February 22).
Manjhi, apparently facing defeat, submitted his resignation to the Governor hours ahead of the trust vote.
She had recently called up Kumar over the Bihar crisis and had assured to fight with him 'if BJP tried to impose President's rule in Bihar'.
The Bihar strong man had congratulated Banerjee recently on her party's victory in the by-election to one Lok Sabha and one assembly seat.