Conversion and Recharacterized are two different things. Did your taxpayer do Both?

Putting (contributing) post-tax funds (nondeductible contribution) into a Traditional IRA and then moving that to Roth is called "backdoor" and is a conversion. It's a way to fund Roth when they don't qualify directly. This second step (the move to Roth) is not a Contribution, because it's the second step.

Recharacterize is when something is contributed, then the nature of that contribution needs to be corrected or changed. An example is putting a nondeductible contribution into Roth, then realizing you don't qualify, so you have it corrected by putting it as nondeductible Traditional IRA. It's still a contribution.

Form 5498 is evidence for money In.

Form 1099-R is evidence for money Out.

"I got 5498 Form that shows Recharacterized contribution amount $6,000"

From which type of account to which type of account?

"and then another 5498 form that shows Roth IRA conversion with the same amount $6,000."

The same amount, or is this is exact same funds?

In other words, did they:

1. Made a Roth contribution

2. Discovered they didn't qualify

3. Recharacterized that to Trad nondeductible IRA contribution

4. Backdoor Roth conversion

Because, as is pointed out, you also need to know if there is any other Trad IRA/SEP/SIMPLE IRA money or was this the only money, and they did a full Roth conversion of all funds not already in Roth? You are going to determine if this is a pro rata conversion (some is taxable, some is not).