I understand that P2SH addresses are used to allow "segwit unaware" wallets to create outputs spendable by segwit wallets (please correct me if I got something wrong). For new clients I think I got it: they will check that the script cointaned in the witness matches the script hash and execute it.
What I do not understand is how this output is spendable by a segwit aware client to the eyes of an old client. Because it clearly doesn't look like an anyone can spend. How does it work?