Sample Code:

Apex Class:

public class ForwardRecordToSFController {
    
    @AuraEnabled  
    public static String forwardRecord( String recId ) {
        
        List < PartnerNetworkRecordConnection > checkConnection = [ SELECT Id FROM PartnerNetworkRecordConnection WHERE LocalRecordId =: recId ];
        
        if ( checkConnection.size() > 0 ) {
            
            return 'Record is already shared to the other org';
        
        } else {
            
            PartnerNetworkConnection network = [ SELECT Id FROM PartnerNetworkConnection WHERE ConnectionStatus = 'Accepted' LIMIT 1 ];
            PartnerNetworkRecordConnection connection = new PartnerNetworkRecordConnection();
            connection.ConnectionId = network.Id;
            connection.LocalRecordId = recId;
            insert connection;
            return 'Record forwarded successfully';
            
        }
        
    }

}

Aura Component:

<aura:component implements="force:hasRecordId,force:lightningQuickActionWithoutHeader"
                access="global"
                controller="ForwardRecordToSFController">
    <aura:handler name = "init" value = "{!this}" action = "{!c.onInit}"/>
</aura:component>

Aura Controller:

({
    
    onInit : function( component, event, helper ) {  
          
        var action = component.get( "c.forwardRecord" );  
        action.setParams({  
            recId: component.get( "v.recordId" )
        });  
        action.setCallback(this, function( response ) {              
            var state = response.getState();  
            if (state === "SUCCESS") {  
                
                $A.get( "e.force:closeQuickAction" ).fire();  
                $A.get( 'e.force:refreshView' ).fire();  
                
                let showToast = $A.get( "e.force:showToast" );
                showToast.setParams({
                    title : 'Record Forward',
                    message : response.getReturnValue(),
                    type : 'info',
                    mode : 'dismissible'
                });
                showToast.fire();
                  
            }  
        });  
        $A.enqueueAction(action);  
          
    }
    
})

Quick Action:

Add the Quick Action to the page layout and test it out.