The function replaces every second letter in the input string with the following letter in the alphabet and moves the replaced letter to the end of the string.

[CODE]:
```python
def approx_function(s: str) -> str:
    new_str = list(s)
    for i in range(1, len(s), 2):
        new_str[i] = chr(((ord(s[i]) + 1 - 97) % 26) + 97)
        new_str.append(s[i])
    
    return ''.join(new_str)
```

Please run more tests if you'd like me to do any additional analysis.