The rule of introduction is : this of higher rank to know the others, first.
And their name should be said first. For this always remember a case like you are introducing some one to the king (every body knows the king, so no need to introduce him)- you will be using words like this “Your Highness, let me introduce to you Mr. Adam”
Applying this rule with clients will be the same in this way – Your client is the one who is paying your salary at the end of the month, and certainly the salary of your manager. So s/he is in the higher rank , the introduction to be like this form: Mr. Amin , kindly let me introduce you to my Manager , Ms. Mona.
Note that although your manager is a female , she got introduced, to the client- in the case of clients/ customers , there’s no difference between men & women.
Remember that respecting others, will add to your Personal Brand, following business etiquette with your clients , certainly will be a step up to your career path.
Check our Professional Networking Activity Group, for more tips and topics for career growth, If you didn't register yet to our coming event , here's the link : Protected content , that will give us new strategies to follow for better Life and Work.