Message-processing rules can be specific to your email client program, or stored centrally on the server. Server rules are the most common. These will always operate regardless of whether your email program is open. All server-side rules will be migrated automatically as part of Nexus move to Nexus365.
Rules which are unique to your email program may need to be updated after you move. This is dependent on the program you're using as well as what tasks the rule undertakes. Microsoft Outlook adds the words 'client only' in brackets after the rules's name, to help you identify those. Client only rules will only work when your email program is running. Non-Microsoft email programs may not distinguish between server-side and client-only rules. No rules will be deleted as part of the move and, depending on what your rules are configured to, most client-only rules should continue to work after it is completed.