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The following codes work.

def LongestPermInDoubleCosetWeylGroupGivenTypeRank(S1,w,S2,typ,rank): # typ='A', longest element in S1 w S2, S1,S2 are generating sets
    W=WeylGroup(typ+str(rank), prefix = 's')
    g1=W.subgroup(S1)
    g2=W.subgroup(S2)
    winner = W.one()
    for u1 in g1:
        for u2 in g2:
            t1=u1*w*u2
            if t1.length()>winner.length():
                winner=t1
    r=winner

    return r

typ='A'
rank=4
W=WeylGroup(typ+str(rank), prefix = 's')
s = W.simple_reflections()
t2=LongestPermInDoubleCosetWeylGroupGivenTypeRank([s[1],s[2]],s[1]*s[3],[s[2]], typ, rank)
t2