The main question is what software your devices were running before.
An iPhone 4S is able to support iPhone call forwarding to FaceTime on a
Mac, but the iPhone had to be running iOS 8.1 or later, the Mac had to
be running OS X 10.10 (Yosemite) or later. The feature has to be enabled
on the iPhone, and the iPhone and Mac must be on the same Wi-Fi network
and signed into the same iCloud account.
The SMS fowarding feature would have also worked (same requirements
except it only needs Internet access, not being on the same Wi-Fi
network).
All the other Continuity features (e.g. AirDrop, Handoff, Instant
Hotspot) require an iPhone 5 or later and a new enough Mac (mid 2012 or
newer), because they use Bluetooth 4.0.
This covers the system requirements for most Continuity features:
https://support.apple.com/HT204689
This covers AirDrop:
https://support.apple.com/HT204144
--
David Empson
dem...@actrix.gen.nz