Here's a NumPythonic vectorized approach -
B[:,1][(A == B[:,0].astype(int)[:,None,None]).argmax(0)]
Sample run on a generic case -
In [118]: A
Out[118]:
array([[4, 3],
[2, 3],
[2, 4]])
In [119]: B
Out[119]:
array([['3', 'Alpha'],
['4', 'Beta'],
['2', 'Gamma']],
dtype='|S5')
In [120]: B[:,1][(A == B[:,0].astype(int)[:,None,None]).argmax(0)]
Out[120]:
array([['Beta', 'Alpha'],
['Gamma', 'Alpha'],
['Gamma', 'Beta']],
dtype='|S5')