How to renew SSL Ceritificate in Send connector in Exchange Server 2013

I have hybrid environment with Exchange server 2013 CU8 and Office 365. Every thing was working fine but after expiring of Public SSL, mail flow from internal users to office 365 and external domains was stopped.
After looking into it more, came to know that send connector was using SSL certificate which was expired, So after renewing SSL certificate, download it on the servers and import it on the server in required certificate store.
then start to assign it to the Send connector
took the following steps.

1. First note the thumbprint of new SSL certificate
2. Note the name of Send connector
3. Use following command to assign it to send connector

$cert = Get-ExchangeCertificate -Thumbprint bbbbbbkhkkjkj1cee4ca68khy28c5b27ut67e7dopu

$TLSCert = "<i>$($cert.Issuer)<s>$($cert.Subject)"

Set-SendConnector -Identity "Default send connector" -TLSCertificateName $TLSCert

after that mail flow start working