Adding HL-NT devices in VLAN to HW4

What do I have to consider so that HL-NT in the VLAN can communicate with HW4? There is a situation where many HL-NT care connected in VLAN. The computers are in one VLAN and HL-NT and PF4 are in another VLAN. If their network is connected to the internet, then HW4 cannot see the devices. If the network is not connected to the internet, HW4 can see all HL-NT.

How should HW4 or the device be configured to run with internet, so the devices can be maintained remote?