An easy way to find the correct shift amount and resultant letter is to assign each letter of the alphabet a number that increments each time. There are several ways to do this. After that, the resultant letter is (current + absolute_value(current - previous)) mod 26 assuming a is 0, b is 1 and so on. Keep in mind that the first character in the input may be a space.

Pseudo Code

char previousLetter = '0';
for (char current : allCharacters) {
  if (current == ' ') print(' ');
  else {
    if (previousLetter == '0') print(current);
    else {
      char newLetter = (current - 'a' + Math.abs(current - previousLetter)) % 26;
      print(newLetter);
    }
    previousLetter = current;
  }
}