Does a non-HP single-mode transceiver work in a HP switch, and does a non-HP single-mode transceiver communicate with a single-mode HP transceiver?
HPE switches with pre-16.x firmware require original or HP-compatible transceivers. A transceiver that's not HPE branded is not activated when inserted, as indicated by LED and in the device log. You don't necessarily need an original HPE module, there's a large "compatible" market with SFPs that electronically claim to be original.
With 16.x firmware you can
allow-unsupported-transceivers. HPE explicitly doesn't provide support if there's a chance that your problem originates from a non-HPE module.
Ethernet standards guarantee interoperability, regardless of vendor or brand. You can use any two 1000BASE-LX transceivers to link with each other, likewise 10GBASE-LR and so on.