Is it a good idea to run UPS using 3rd party battery? (updated with pic)

I have a suburban home where the power supply isn't very stable. My current UPS is APC 1500Pro. With its builtin battery, my network device including surveillance cameras can last 3 hours after the power is lost, which isn't enough for me to get my ass there and hook it to my car as power source. So I'm thinking about replacing the two builtin batteries with two bigger batteries which has standby voltage around 13.8V

https://www.amazon.com/POWER-SONIC-PS-12180-F2-Battery-Terminal/dp/B00FA5Z17W/ref=sr_1_6?crid=3AIVV7... Opens a new window

Before I start doing so, can I get some suggestion on if it's safe to do so or if the battery is compatible at all?

Thanks!

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Updates: Thanks everyone for the reply. I read every one of the comments and seems the result is quite different for different people. I'll probably give it a try in a controlled...