What if he/she works as an assistant of Mr. Z? Then it might be in her/his job description to make phone calls for Mr. Z. At least that is how it works where I live.
It's one of the issues that I have with "authority" or "grades" in workplaces. I do understand that this man is the boss of the company and if I were working as his assistant and he asked me to
make a phone call for him, I would have no problem with that. I would expect to telephone the person concerned and have a conversation with them on behalf of my boss. Perhaps the person I would telephone would be the assistant to a boss of another company and we would talk to each other about certain issues. We would then pass the contents/details of our conversation on to our respective bosses. Clearly, on that basis, I have some responsibility and I would feel like a valued member of his team/staff.
If he simply expected me to pick up the telephone, dial the numbers, and then as soon as the other boss was on the phone, transfer the call to him, I would be extremely unhappy. Those are more like the actions of "master and servant", not a boss and his valued assistant. I would not expect the personal assistant of a the boss of a company to be employed to carry out such menial tasks.
No-one is too busy to dial a few numbers on a telephone themselves. I'm sure if he is that important then he probably has a direct number for the other boss and doesn't actually need someone to call the company, speak to the receptionist, speak to the other boss's personal assistant and then put the call through to him. If he is simply too lazy to pick up the phone and make the call himself, then I wouldn't consider him worth working for.
In my previous job, I held a fairly responsible position within the British Civil Service. I had earned my position and it warranted a certain amount of respect. On my first day at a new office back in 2002, my immediate superior at that office handed me a piece of paper and said "Fax that". After a brief pause, I handed it back and said "No". He looked at me in astonishment. I pointed out that I was only one grade below him, was a valued and quite high-ranking member of the department and that I was pretty sure that "faxing stuff" wasn't in my job description. I pointed out that there were a number of administrative staff who were actually employed to send faxes and to answer the phone and I was sure that one of them would be delighted to fulfil his request. It worked and he didn't ask me to do such a menial task in the future. I should point out that I actually never asked the admin staff to send a fax that I had written and printed out. As far as I was concerned, it was my fax and up to me to send. I always sent them myself because I simply could not bring myself to appear so lazy that I couldn't shove one piece of paper into a fax machine and press a few buttons.
I will step down off my soapbox now, you'll be pleased to know.
As far as the original question goes, if it is indeed that person's responsibility to do so, I would say:
"Good morning/afternoon. This is Jim Brown, personal assistant to Bob Fox at Macrosoft Limited. Mr Fox would like to speak to Mr Jones. Could you put me/him through please?"