I don't know how you application works, but there are the information about certificate for Outlook client, it may similar to your application:
For Exchange server, when client want to build a connection with it, the connection will using server side certificate to encrypt the connection. If you are using a certificate which issued by a personal CA, you will need to install the certificate on client side.
In your environment, the certificate is issued by Office 365 which is a public CA, the certificate will be trusted by client by default, you don't need to install certificate on client side.
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