To ensure that the hex is always 40 characters long, the BigInteger has to be positive:

public String toHex(String arg) {
  return String.format("%x", new BigInteger(1, arg.getBytes(/*YOUR_CHARSET?*/)));
}

The issue here is that you're trying to create a String from binary data, and the default encoding used by the String class is changing the value of that binary.

Example:

String output = new String(new byte[]{(byte)0x90, (byte)0x81, (byte)0x8d, (byte)0x8f, (byte)0x90, (byte)0x9d});
System.out.println(DatatypeConverter.printHexBinary(output.getBytes()));

Output:

3F3F3F3F3F3F

Hang on to the byte[] that parseHexBinary outputs and set a breakpoint so you can examine it's contents directly, you'll notice that it contains the correct binary values.

Update per comments:

If you want to write the output of parseHexBinary to a file, you should write the raw bytes to the file, not a String of the bytes.

DataOutputStream os = new DataOutputStream(new FileOutputStream("someFileName"));
byte[] bytes = DatatypeConverter.parseHexBinary(input);
os.write(bytes, 0, bytes.length);
os.close();

byte[] bytes = javax.xml.bind.DatatypeConverter.parseHexBinary(hexString);
String result= new String(bytes, encoding);

Is this what you are looking for?

Integer.toHexString(Integer.parseInt(String));