During AU week, it would make things easier if B knows A' as either the person they have always known or a complete stranger, unless there is something that you feel absolutely precludes it -- in that case, though, it would be vital to talk things over with A-mun to agree on what degree of memory B retains of A while encountering A'. It is, however, more fun to simply accept A' at face value and meet them over. Actually, 'meeting over under different circumstances' was a favourite leitmotif of the AU weeks in Morningstar Manor, especially for established relationships (of any kind), right next to 'friends as enemies' and 'enemies as lovers'.