This may solve the issue
IFeature pNewAnnoFeature = pFeatureClass.CreateFeature();
if (CopyAttributes(pOldFeature, ref pNewAnnoFeature, out outErrMsg) == false)
{
MessageBox.Show(outErrMsg);
return;
}
IClone pFirstAnnotation = (IClone)(pOldFeature as IAnnotationFeature).Annotation;
IElement pSecondElement = pFirstAnnotation.Clone() as IElement;
ITextElement pSecondTextElement = pSecondElement as ITextElement;
try
{
//ensure the alignment of the cloned text is lower left
ISymbolCollectionElement txtSymElemTwo = (ISymbolCollectionElement)pSecondTextElement;
txtSymElemTwo.HorizontalAlignment = esriTextHorizontalAlignment.esriTHALeft;
txtSymElemTwo.VerticalAlignment = esriTextVerticalAlignment.esriTVABottom;
}
catch (Exception ex)
{
MessageBox.Show(ex.ToString());
}
ITransform2D pTransform2D = (pSecondTextElement as ITransform2D);
pTransform2D.Move(100, 100);
(pNewAnnoFeature as IAnnotationFeature).Annotation = pSecondElement;
pNewAnnoFeature.Store();