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The laptop is an Intel Skylake platform (6th Gen).
HP EliteBook 840 G3 Notebook PC - Maintenance and Service Guide
There are apparently different versions, but all have a DisplayPort Dual-Mode (DP++) connector:
This means that you can plug a (cheap) passive cable from DisplayPort to HDMI, but this has the limitation that only the bandwidth that the processor can deliver with the HDMI protocol is available. In this case, 300 MHz TMDS (theoretically 4K @ 30 Hz).
However, the processor can also output the DisplayPort 1.2 HBR2 protocol. So if you use an active cable that acts as a protocol converter, it should be possible to get a resolution of 4K @ 60 Hz on the Philips 50PUS7609.
Please note: HDR is not supported by Skylake processors.
I would recommend one of the following active cables (DisplayPort > HDMI). They should work plug and play. If not, please use the relevant hot key to switch the screen image among display devices connected to the system. If the TV is connected to the computer, pressing and holding Fn (at the bottom left) + pressing F4 shortly (at the top of the keyboard with monitor symbol) will alternate the screen image from laptop display to the TV. On repetition to both. Or back.
- Club 3D CAC-1082 ... (2 meters / 6.56 feet)
- Club 3D CAC-1087 ... (3 meters / 9.84 feet), also suitable for modern sources up to 8K
- Cable Matters 102103 ... (2 meters / 6.56 feet), also suitable for modern sources up to 8K
