Carrier Sim Card Question

I'll try to not make this confusing.

First the facts:
1. My wife has an iPhone 5S
2. I have an iPhone 6 Plus
3. I bought an iPhone 7 Plus
4. AT&T is my carrier

OK, I get my iPhone 7 Plus (which has a new sim card in it). I activate and set up my new phone. Cool, no problems.

Next, I erase the iPhone 6 Plus and take the SIM card out. I take the SIM card out of my wifes phone (iPhone 5s) and insert it into the iPhone 6 Plus (she gets my handme downs). I set her phone up and all is still well.

Finally, I take my OLD SIM card out that was in my original iPhone 6 Plus and place it into the iPhone 5s and erase that phone.

My question now is...my wife is going to give the old iPhone 5s to a co-worker at her work and the person just called me to ask if they needed a NEW SIM card (from the ATT store), of could they use the one currently in the phone. I don't know...

Isn't the SIM card just for activating the phone...does it even matter? Should the person go get a new SIM card?

--- Post Merged, Sep 29, 2016 ---

Also...any other tips to make it easier for someone with the transition for this person that is not used to an iPhone. Thanks.