My mom called AMO Recoveries to see if she could make a payment arrangement with them, the lady was very rude and said they will not make payment arangements with her and that she needed to pay immediately, otherwise her credit will be affected. What can she do about it?

Yes, they can refuse payment arrangements, that is part of their "firm demand for the balance in full" (collections training 101). I seriously doubt, however, that were she to send in a check/MO, that they would refuse to cash it. If an account is in collections, then would it not already be on her credit? They are allowed to only report accurate information on her credit report, unless she can negotiate something better.

What can she do about it?

-Try to negotiate with the CA. Start out lower than she can really pay, but I'd advise to never set up automatic check withdrawl, and never get a PDL to pay a bill. As a collector, I hated snail mail, but as a debtor, it's the only way I'll pay.
-Ensure her rights under the fdcpa and billing laws are not being violated (for example, threatening arrest, calling too often, incorrect amounts, etc...).
-If she's upset about the collector being rude, I'd advise your mom to be always be calm on the phone, and drag on the call as long as she possibly can. Time is money, so if the collector is being rude, but staying within the law, that is probably the best way she can get even with the person on the other end of the phone. In my office, no one gave a rat's butt about a collector being rude, I don't see that changing for any other call center, either.

Someone else should be along soon, and I'm sure they can offer more advice on negotiations. My experience was collecting a certain type of debt that was not negotiable--PIF was just about the only way to clear up the matter.

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The only people with whom you should try to get even are those who have helped you.
-John E. Southard

Before giving a collector any money,validate the freaking debt people! Another thing is stay off the phone! Send them debt validation letter certified return receipt. This letter enforces your rights and make collector prove a few things to the consumer:
1. That you are indeed the correct debtor for account.
2. They have right to collect on this account.
Insert clause stating inconveinant to call me and communicate by written method only. Do not ever give banking info to a collector.Use money order or certified checks only.

Once a collector has validated your debt account, they have authorized reasons to hit your credit copy. The reporting from them will lower down the scores. At this point, the damage is already done to your credit. Make payment even if they are not willing to work on your arrangements. Once you send them money, it is illegal not to post it towards your account. Otherwise, you can throw a case on them for pocketing your money and not posting it towards your account. Make sure that the amount you send them is reasonable and there is a receipt or the bank statement showing the payment done.

I agree with Rblandon4, if you were to send in a check or mo, they will not send it back! Also, be sure to get it validated. Once you start sending regular payments to them, they might ease up on the harrassing calls. Another question, have you recieved any type of notice or letter from them regarding the debt?? I would also contact the original creditor to see who is collecting on the debt for them.

Not all collection agencies report to the CBR's but they have the option to. It depends on the client and if they own the debt or not.