Yes but when I say it’s insten, you can look for the actual seller being insten
Insten Rechargeable Replacement Battery 1200mAh 3.6V Compatible with Sony PSP 3000 / PSP Slim 2000, Include Model PSP-2001, PSP-3000, PSP-3001, PSP-3002, PSP-3004 https://www.amazon.com/dp/B00QGTUILU/ref=cm_sw_r_cp_api_glt_fabc_QT85V0YV7ETY4WGBHNDT?_encoding=UTF8&psc=1
Insten Rechargeable Replacement Battery 1200mAh 3.6V Compatible With Sony PSP 3000 / PSP Slim 2000, Include Model PSP-2001, PSP-3000, PSP-3001, PSP-3002, PSP-3004 https://www.amazon.com/dp/B00QGTUILU/ref=cm_sw_r_cp_api_glt_fabc_DF6CM7S6C55FQC3AZTSD?_encoding=UTF8&psc=1
Hi
Extremely sorry for the late reply.
The 3001 is much more harder to find a decent replacement battery for. Having said that your main option is to go for this one : https://www.amazon.com/Rechargeable-Replacement-Compatible-Sony-PSP-PSP-2001/dp/B00QGTUILU?ref_=Oct_BSellerS_11076451_0.
It is made by an company called Insten and they seem to be good at referbishing old batteries, but it can be hit and miss sometimes. Try using it as much as you can with the Amazon 30 day returned policy (even if it means charging it, and then leaving the PSP on with a game loaded to eat through the charge). This will help you see if the new battery would last. Rinse and repeat on the second try, if it comes down to it.
Let me know how you get on.
I've only been using this one for a couple of weeks so I can't speak to its longevity but I'm happy with it so far. My longest play session was over 3 hours without it dying.
https://www.amazon.com/dp/B00QGTUILU/ref=cm_sw_r_cp_awdb_btf_t1_wL8AFbZXVXGA2
Aftermarket, specifically this one from Insten. I was hesitant cause the reviews are mixed, but I've been getting 4-6 hours of gameplay with it on my PSP 3000, although the fact that I rip my UMDs to my MemoryStick is definitely a factor in that since I'm not using extra power to run the UMD drive. (BTW, I'd recommend you rip your UMDs as well since not only do you get improved battery life, but also the benefit of having all your games right there on your system. Modding a PSP and ripping games is super easy, and I can send some video tutorials if you're interested.) If the battery doesn't work properly you can always return it to Amazon.
I mean I bought one off of amazon but I'm not sure about shipping for you and it ain't great either, probably only holds 80-90% of the original's charge but if you wanna try I can only link to the US amazon page so you may have to do some digging for it, Here's a Link. And this one somehow works with all models you just have to slice This little nub off (Sorry About the janky circle I literally Did it in paint)
I got it here. It’s an awkward fit in my 3001, but it seems to hold a charge!
I couldn't find the KMD slim model on amazon or ebay, the only place where I got em where from Mercado Libre which is like latin america version of ebay. So I added a link to an insten battery, which also worked greak for a generic brand.
https://www.amazon.com/Rechargeable-Replacement-Compatible-Sony-PSP-PSP-2001/dp/B00QGTUILU/ref=sr_1_1_sspa?crid=2BAOXMEEM895Z&dchild=1&keywords=kmd+psp+battery&qid=1605210722&sprefix=kmd+psp%2Caps%2C201&sr=8-1-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExMjc4SEpJSjZSUU8mZW5jcnlwdGVkSWQ9QTAxNzM2MDVUWVcyNVIxOVk0SEomZW5jcnlwdGVkQWRJZD1BMDI2MDgzMDNQM1A2SlFGMUVRVUUmd2lkZ2V0TmFtZT1zcF9hdGYmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl
Some people don't feel comfortable clicking links, in that case you could also type Insten psp battery on amazon and it should be the first one to appear. just double check it says for psp 2000 or 3000 models, 1000 model will not fit your psp.
I've been using this one for a few months, it's ok, I get about 3 hours out of a charge. I can't speak for longevity though.
Off amazon. Insten Rechargeable Replacement... https://www.amazon.com/dp/B00QGTUILU?ref=ppx_pop_mob_ap_share
Here’s a non-ref link to the product on amazon: https://www.amazon.com/Rechargeable-Replacement-Compatible-Sony-PSP-PSP-2001/dp/B00QGTUILU/ref=mp_s_a_1_3?keywords=psp+3000+battery&qid=1571424152&sr=8-3
I bought this third party battery for my 3000 and it works great, should fit in your 2000 model just fine.
I'd also highly recommend getting a MicroSD to MemoryStick adapter, as MicroSD cards are way cheaper than official MemorySticks (this 64GB one is £10 and is way more than enough storage for your needs).
And once you have those, I highly recommend installing custom firmware onto your PSP, which allows you to copy your UMDs to your MemoryStick and play them off there (which adds the benefits of not only having all your games with you, but also improved battery life since you're not using the UMD drive). You can also do this for your UMD movies.
EDIT: Fixed the malformed link.