Is it safe to reuse a phone battery after removing it?

Hey guys!

So I removed my original phone battery because whenever I charged it , my phone would overheat too much without a fan.

However I bought a faulty battery which ive now returned and stuck without a phone …

I’m able to get a new phone in a month so I'm not keen on buying another faulty “Genuine battery” from ebay again haha xD

I was wondering if I could just place my original battery back into my phone and I will carry on using the fan whenever I charge it.

Is this safe?

Many thanks!