...
MemoryStream streamReader;
...
myClass.mapdrive();
byte[] buffer = new byte[4096];

using (FileStream streamWriter = File.Create(@"\myserverthesharemyfile.txt"))
{
    StreamUtils.Copy(streamReader, streamWriter, buffer); //<-- Point of Exception (Access Denied)
}

public class myclass
{
    public static void mapdrive()
    {
    System.Diagnostics.Process p = new System.Diagnostics.Process();
        p.StartInfo.UseShellExecute = false;
        p.StartInfo.CreateNoWindow = true;
        p.StartInfo.RedirectStandardError = true;
        p.StartInfo.RedirectStandardOutput = true;
        p.StartInfo.FileName = "net.exe";
        p.StartInfo.Arguments = String.Format(
                    "net use %1 %2 /USER:%3",
                    @"\myservertheshare",
                    "passme",
                    @"\myservermyuser"
        );
        p.Start();
        p.WaitForExit();
    }
}