Can we use SQL Express to send messages to SQL Standard using the Service Broker?
The 'client only' means that two Express instances cannot communicate directly. They have to have a Standard instance in between acting as a forwarder. Express instances can both generate and consume messages. 


Messages originating on Express instances can be received on Standard or higher instances.
Messages originating on Standard or higher instance can be received on Express
Messages originating on Expres can be received on another Express instance only if it was routed to an intermediate Standard or higher instance using a forwarding endpoint, see Service Broker Message Forwarding. A single Standard instance can act as a forwarder to any numer of Express instances, limited only by processing capacity and network bandwidth.