Hi,
In theory any iPhone that has the Apple ID should link that device to the set up.
However have you changed the Time Zone on the second iPhone ?
All iMessages are time stamped which in turn is based on the Location and Country Code set up for your iPhone and Mac.
On the Mac it is in Messages > Preferences > Accounts > iMessages account and using the Details Button and logging in (again as it were).
If they don't match you are unlikely to see some messages.
9:23 pm Thursday; June 4, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad