I think I found a solution:

The following code allows to convert .Net abbreviated enumerable values into
their original format. Hope this will help someone.

//  *** code start ***
using System;
using System.Collections;

public class xmlEnumAttributes
{
    private ArrayList _abbrevs = new ArrayList();
    private ArrayList _values = new ArrayList();

    public xmlEnumAttributes(Type enumType)
    {
        if (!enumType.IsEnum)
        {
            throw new ArgumentException("Not enumerable type.");
        }

        foreach (System.Reflection.MemberInfo info in enumType.GetMembers())
        {
            //    I think we can safely assume only one XmlEnumAttribute per enum value
            foreach (System.Xml.Serialization.XmlEnumAttribute att in
info.GetCustomAttributes(typeof(System.Xml.Serialization.XmlEnumAttribute),
true))
            {
                _abbrevs.Add(info.Name);
                _values.Add(att.Name);
                break;
            }
        }
    }

    public string GetValue(object abbrevValue)
    {
        string abbrev = abbrevValue.ToString();
        int index = _abbrevs.IndexOf(_abbrevs, abbrev);
        return (index > -1) ? _values[index] : null;
    }
}

//    example of using the class:
//    if myXmlDeserialisedObject.enumerableValue is of myEnum type

xmlEnumAttributes myEnumValues = new xmlEnumAttributes(typeof(myEnum));
string value = myEnumValues.GetValue(myXmlDeserialisedObject.enumerableValue);

//   ***end of code segment ***

PS I have only used string enumerated values and therefore the code for
other enumerated types may require different code. Also If anyone could
specify a better solution to the problem in my original post, I would really
appreciate that.