The due date is extended up to 31st August 2019. Yes ITR needs to be filed. However, it has to be filed in your capacity as Legal Heir. There is a procedure to do so. It is better that you engage the services of a Chartered Accountant and provide him full details of the income during the financial year.
Further, if you have inherited any assets and same are giving you income in India like rent, dividends or interest, such income needs to be credited first to your NRO account and later can be repatriated back to you to a maximum of USD 1.00 million subject to the submission of forms 15CA and 15CB to the Bank handling the remittance.