The investor, Pankaj Shroff, submitted a copy of the purported mail while opposing the bail applications of Shah and former FTIL CFO Shreekant Javgalgekar who is also an accused.
Further hearing on the pleas is likely on June 18.
Shroff's lawyer Sandeep Karnik told the court that in one of the mails Sinha told Shah and Javgalgekar that NSEL had got bogus profit of Rs 6 crore from N K Proteins Ltd.
Shah had earlier blamed Sinha for the payment crisis at the NSEL.
Shah, whose firm FTIL is the promoter of NSEL, and Javalgekar were arrested on May 7 and are currently lodged in high-security Arthur Road jail.
Shah came under the scanner of Economic Offences Wing (EOW) and other agencies last year when NSEL faced a payment crisis and nearly 18,000 investors allegedly lost crores of rupees.
Besides being the founder Chairman and group Chief Executive of Financial Technologies Group, Shah is also the founder of MCX, the world's eighth largest commodity futures exchange.