Languages Switcher between websites

Hi www.remarpro.com community.

I have got the idea yesterday to add new a language to my website, and I have been searching the internet for the best way and I found the best way is to make a new wordpress installation with that language in a subdomain with the language code.

My english wordpress is: https://abdgd.com
My Arabic wordpress is: https://ar.abdgd.com

The both sites are exactly the same but with two diffrent language and diffrent database, users, link, folder.

I am done with everything in the new website and made it easy, when you add ar. to the link it gets in the new language, because I set the perma links and the pagelinks the same as the English version.

Ok, here comes the problem:
I have added the new website link (Arabic – ???????) to the English website main menu and when users click on the link the site gets in arabic but it goas to the main page.

My problem here is I want it to stay in the same page but just change from abdgd.com to ar.abdgd.com when clicking the link.

We take an exemple:
https://abdgd.com/services/

here is the english version of my service pages that I offer to customer.

I want it to get to https://ar.abdgd.com/services/ when clicking the link in the menu and not to the main page in the arabic version https://ar.abdgd.com/

I have searched all over the internet and in the forums with no luck, I hope I gave you the needed information and I hope you got my idea.

Thank you, Best Regards ABD Graohuc Design.