Frame challenge
I would like to start with a frame challenge, as this is how I design my systems: an administrator should not be able to change other user's passwords. Of course the standard caveat applies: we all have different needs, and depending on what your system is storing, convenience may trump security and letting an admin change user's passwords might be the best choice for your business. However, I would say that if there is anything of value in the system then an administrator should not be able to change a user's password.
Instead, your system should have simple self-service password reset capabilities using modern best practices. In the event that someone is completely locked out of an account you can always create a separate "Account recovery" process that requires separate verification of identity and takes at least a few business
days to get through (a slow account recovery gives the actual account owner time to respond if the attempted account recovery is not actually legitimate). Again, YMMV, and the techniques you employ will obviously depend upon the value of what your system is protecting.
The main reason for this is because allowing admins to change passwords can effectively destroy audit trails. "Administrator" doesn't (and shouldn't) mean "Has full access to absolutely everything", and allowing them to change a user's password potentially gives them the ability to evade any built-in auditing you have by taking over another user's account directly.
Finally, giving an admin the ability to change user passwords makes them a target for social engineering attacks if an attacker wants to gain access to someone else's account. Allowing admins to make changes to accounts is basically what landed AT&T in a $240 million lawsuit over crypto currency theft: https://www.theregister.co.uk/2018/08/15/att_sued_cryptocurrency/
Answering your question
Still, the best answer is not the only answer, so I wanted to answer your actual question. If you are going to give admin's the ability to change a user's password, whether or not you also ask them to provide their password to change the user's password depends on what you are trying to protect against.
The whole point of asking for a user's password when they change passwords is to protect against further privilege escalation if someone gets access to the user's session. Whether it is by stolen cookies or simply waiting until someone walks away from their computer with it unlocked, an attacker who gains authenticated access to someone's account could go and change their password to make their access permanent. Asking for the user's password before allowing a password change makes that much harder. The attacker is still in the system, but they can't lock out the original user and can't make their access permanent.
The same rule applies here, and therefore your choice depends on how secure you want this to be. If your admin works in the office, gets up for lunch, and leaves his computer unlocked and still logged in, then anyone could sit down and start changing user passwords. It's even better if they can go change another admin's password - then they have permanent admin access. Of course they could also just create another account and make themselves admin, giving themselves permanent access.
One way to prevent those kinds of attacks would be by asking the admin for their password before allowing sensitive changes (changing their password, changing another user's password, creating more admins, etc...). Ultimately though it is up to you to decide how to balance convenience vs security for your organization.
