How to play games with 90hz or 120hz while connecting to capture card?

[sonwid23]

Elgato doesn't have higher refresh rate than 60hz
So when Rog phone connects through Type-C to HDMI Adapter to Elgato
Rog phone gets fixed 60hz, It can't be adjusted
(I think Oneplus gets any refresh rate without being affected by the capture card. But I'm not sure that refresh rate is real)

Now questions,
If Rog phone connects to capture card of Avermedia GC553, can Rog phone get higher refresh rate than 60hz? (Sorry, I can't add link, GC553 allows 4k60hz, 1080p120hz)
Is there any way to get refresh rate which can be adjusted without being affected by the capture card like Oneplus?
Any ideas?

[Danishblunt]

Did you try both ports?
Also whats important here is that you have a high quality 4k60 cable / adapter, if you have a cheap cable you might get stuck at 1080p60 due to limitaions.

[sonwid23]

nightmaster552

Did you try both ports?

Also whats important here is that you have a high quality 4k60 cable / adapter, if you have a cheap cable you might get stuck at 1080p60 due to limitaions.

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Yea, I ordered this Adapter in Amazon
▶ Cable Matter USB to HDMI Adapter (USB-C to HDMI Adapter) Supporting 4K 60Hz and 60W Charging black

Also, I have already good HDMI Cable too
Btw, In that adapter's description, "Supporting 1080p120 or 1080p90" is not written
So I'm worried It won't support 120Hz or 90Hz
If some adapter supports 4K 60Hz, that adapter also supports 1080p90Hz in usual?
and If I have all that products can Rog phone get 90Hz or 120Hz when It's connected to capture card?
thank you for answer