A generator for mapping of last to first column in BWT matrix. Input is a BW transform of DNA sequence.

BWT_First_To_Last.py

#change this if you want to support other types of sequences
def get_char_index(c):
    if c == 'A':
        return 1
    elif c == 'C':
        return 2
    elif c == 'G':
        return 3
    elif c == 'T':
        return 4
    elif c == '$':
        return 0
    else:
        return -1

def get_last_to_first(bwt):
    counts = [0, 0, 0, 0, 0]
    letter_pos = list()
    for c in bwt:
        index = get_char_index(c)
        letter_pos.append(counts[index])
        counts[index] += 1
    cum_counts = [sum(counts[:i]) for i in range(len(counts))]
    for i in range(len(bwt)):
        letter_pos[i] += cum_counts[get_char_index(bwt[i])]
    
    return letter_pos

def get_first_col(bwt):
    letter_pos = get_last_to_first(bwt)

    answer = [None] * len(bwt)
    for i in range(len(bwt)):
        answer[letter_pos[i]] = bwt[i]
    return ''.join(answer)

More information about BW transform: Wikipedia.
A useful resource for this algorithm: Lecture from Stanford