public void TransferAttributes( 
   MapMember source,
   long sourceOID,
   MapMember target,
   long targetOID
)

var transferAttributes = new EditOperation() { Name = "Transfer Attributes" };

// transfer attributes using the stored field mapping
transferAttributes.TransferAttributes(featureLayer, oid, destinationLayer, targetOID);

// OR transfer attributes using an auto-match on the attributes
transferAttributes.TransferAttributes(featureLayer, oid, destinationLayer, targetOID, "");

// OR transfer attributes using a specified set of field mappings
//  dictionary key is the field name in the destination layer, dictionary value is the field name in the source layer
var fldMapping = new Dictionary<string, string>();
fldMapping.Add("NAME", "SURNAME");
fldMapping.Add("ADDRESS", "ADDRESS");
transferAttributes.TransferAttributes(featureLayer, oid, destinationLayer, targetOID, fldMapping);

// OR transfer attributes using a custom field mapping expression
string expression = "return {\r\n  " +
    "\"ADDRESS\" : $sourceFeature['ADDRESS'],\r\n  " +
    "\"IMAGE\" : $sourceFeature['IMAGE'],\r\n  + " +
    "\"PRECINCT\" : $sourceFeature['PRECINCT'],\r\n  " +
    "\"WEBSITE\" : $sourceFeature['WEBSITE'],\r\n  " +
    "\"ZIP\" : $sourceFeature['ZIP']\r\n " +
    "}";
transferAttributes.TransferAttributes(featureLayer, oid, destinationLayer, targetOID, expression);

//Execute to execute the operation
//Must be called within QueuedTask.Run
if (!transferAttributes.IsEmpty)
{
  var result = transferAttributes.Execute(); //Execute and ExecuteAsync will return true if the operation was successful and false if not
}

//or use async flavor
//await transferAttributes.ExecuteAsync();