public void CopyAndAddConnectedAsset(Material sourceMaterial, Material targetMaterial)
{
   Document doc = targetMaterial.Document;

   // Get the appearance asset of the source material

   ElementId otherAppearanceAssetId = sourceMaterial.AppearanceAssetId;

   AppearanceAssetElement otherAssetElem = doc.GetElement(otherAppearanceAssetId) as AppearanceAssetElement;

   Asset otherAsset = otherAssetElem.GetRenderingAsset();

   // Get the connected asset of the source material appearance asset (that contains the bitmap)

   AssetProperty otherGenericDiffuseProperty = otherAsset[Generic.GenericDiffuse];

   Asset otherGenericDiffuseConnectedAsset = otherGenericDiffuseProperty.GetSingleConnectedAsset();

   using (Transaction t = new Transaction(doc, "Change a connected asset by a copy"))
   {
      t.Start();

      using (AppearanceAssetEditScope editScope = new AppearanceAssetEditScope(doc))
      {
         ElementId appearanceAssetId = targetMaterial.AppearanceAssetId;

         Asset editableAsset = editScope.Start(appearanceAssetId);   // returns an editable copy of the appearance asset                   

         AssetProperty genericDiffuseProperty = editableAsset[Generic.GenericDiffuse];

         // Find the connected asset (with a shortcut to get the only one)

         Asset genericDiffuseConnectedAsset = genericDiffuseProperty.GetSingleConnectedAsset();

         if (genericDiffuseConnectedAsset == null)
         {
            // Target material has only a color for �GenericDiffuse�
            // This will assign a bitmap to it instead
            // by making a copy of the asset and use it as connected asset
            genericDiffuseProperty.AddCopyAsConnectedAsset(otherGenericDiffuseConnectedAsset);
         }       

         editScope.Commit(true);
      }

      t.Commit();
   }
}

Public Sub CopyAndAddConnectedAsset(sourceMaterial As Material, targetMaterial As Material)
    Dim doc As Document = targetMaterial.Document

    ' Get the appearance asset of the source material


    Dim otherAppearanceAssetId As ElementId = sourceMaterial.AppearanceAssetId

    Dim otherAssetElem As AppearanceAssetElement = TryCast(doc.GetElement(otherAppearanceAssetId), AppearanceAssetElement)

    Dim otherAsset As Asset = otherAssetElem.GetRenderingAsset()

    ' Get the connected asset of the source material appearance asset (that contains the bitmap)


    Dim otherGenericDiffuseProperty As AssetProperty = otherAsset(Generic.GenericDiffuse)

    Dim otherGenericDiffuseConnectedAsset As Asset = otherGenericDiffuseProperty.GetSingleConnectedAsset()

    Using t As New Transaction(doc, "Change a connected asset by a copy")
        t.Start()

        Using editScope As New AppearanceAssetEditScope(doc)
            Dim appearanceAssetId As ElementId = targetMaterial.AppearanceAssetId

            Dim editableAsset As Asset = editScope.Start(appearanceAssetId)
            ' returns an editable copy of the appearance asset                   
            Dim genericDiffuseProperty As AssetProperty = editableAsset(Generic.GenericDiffuse)

            ' Find the connected asset (with a shortcut to get the only one)


            Dim genericDiffuseConnectedAsset As Asset = genericDiffuseProperty.GetSingleConnectedAsset()

            If genericDiffuseConnectedAsset Is Nothing Then
                ' Target material has only a color for “GenericDiffuse”
                ' This will assign a bitmap to it instead
                ' by making a copy of the asset and use it as connected asset
                genericDiffuseProperty.AddCopyAsConnectedAsset(otherGenericDiffuseConnectedAsset)
            End If

            editScope.Commit(True)
        End Using

        t.Commit()
    End Using
End Sub