Yes. I monitor my sons wallet from my phone and he has it on his phone. He can transact so can i.
Discussion
it used to be a problem in the old days with nondeterministic keychains, wasn't possible, in fact, the whole wallet was one big long set of private keys, but with a HD keychain you can have multiple instances they use the same derivation paths and are for all intents and purposes two gates to the same wallet