Yes, you can sell it through Zerodha. The shares will be transferred to your Zerodha Demat account and it will reflect in your Kite holdings, from where you can sell it.
No docs required to be submitted to Zerodha from your end. But the transferred shares will be discrepant in your holdings without a purchase price and purchase date. Follow the steps here to update the purchase price and date so your P&L reflects correctly.