problem in website and outlook connectivity after office 365 migration

Do you have hybrid configuration?
After migration did you reconfigure outlook?
Your internal domain name and external domain name is same?
How did you add domain to O365? Added manually or added by signing into your DNS registrar from O365?

You have MS managing your DNS.

Log in to your portal as an admin. Go to Settings > Domains and click on your domain. You will get a window to update your dns.  Point the domain A record to the IP of your website.

For outlook, you need to update your account information with your new username, password and ms365 server information.

Thank you Scott 
1-what about if I like to manage my dns by myself option  and what records that may cause outlook is not working
2-as what is the case if I leave microsoft manage my dns in details
3-Do Usually it takes 24 hours for email and website to work

waiting for more info from experts   

Thank scott
1-do you mean that website and emails are down for hours after change or only website ??
2-what are records that I need to add excatly for emails  owa/outlook/lynch/autodiscover in office 365
waiting for more info

I think changing the nameserver takes longer than just changing the A  record. But this depends on the service. I have seen it take affect almost instantly and other times longer.

The only thing you need to change is the A record to point to the IP of the webhost.

Hi scott
I did and I cannot access the website and not pinging it??even after nslookup I find it is mapped but  cannot access or ping
what will be the cause of the issue??
waiting for your kind reply

There can be multiple issues.

1) Double check that the web server is setup, that there is a page or index page and note the IP.

2) Using the Microsoft365 Portal, locate the DNS area as I have showed you and make sure there is an A record that points to that IP. Make sure there is only one A record for the domain. Subdomains can have separate A records.

3) After you have made those changes, verify they have been made using a tool like mxtoolbox https://mxtoolbox.com/SuperTool.aspx?action=mx:experts-exchange.com&newAppVersion=1 

4) Once you see the correct information in your lookup tool and you are still not able to see your site, clear your browser cache or better just restart your computer.

5) If you are still not able to view your site, see if you can view the site on your phone NOT connected to your wifi or if somebody from outside of your network/building is able to view the site. If this is the case, then you have a firewall issue.

I will do dns at my registrer as I have my website
Do the website will take time as A record and name server will update??
Also I want to receive answers from multiple experts ??

I will do dns at my registrer as I have my website
Do the website will take time as A record and name server will update??

There is no telling. Most of the time it is within minutes and sometimes it is longer and there is always the potential for 72 hours but I have not seen that since the 90's.

Also I want to receive answers from multiple experts ?? 

What is it you need to hear?  This is getting confusing. You said you did a migration to Microsoft365 (Formerly Office365) and that your website does not work.  I gave you the potential reasons, either you do not have an A record pointing to your site or you have the A record pointing to your site but you do not have the webserver setup correctly Or you have a firewall issue if you can see the site outside of your network.

Now you are talking about moving the nameserver to your hosting company. That may break some of your Microsoft365. Make sure to note the current DNS information and copy it over.  

At this point, there is not a succinct problem to tackle.  Your next step is to move the nameserver over and go from there.  

FOA technically your migration of mailboxes has nothing to do with your website config or your OWA.
That is why I asked you some details in my first comment.
Can you ping your website from inside and outside network? Make sure you get same IP address from inside and outside network.

ping www.yourexternaldomain.com

Select allOpen in new window

Ensure it is pointing to your hosting company IP address.