help with my emails

[Cupcakemumma]

New to the board.
I have a website hosted by a provider and unfortunately they are not answering my emails.
So I'm thinking of changing my website provider but is there any way I can still access my round cube hosted emails.  I have the password but I'm trying to log in and I get this error.

Does anyone have any suggestions as to how I can access my emails or are they lost

Any help would be appreciated.
I am not completely computer illiterate but I'm not super savvy either. 
Thank you so much for any assistance .

[JohnDoh]

Roundcube is opensource webmail software, not a service. Your provider is using it to give you web based access only. Your provider hosts your mailbox. If you know the IMAP details then you can use any IMAP client to access your mailbox. Then you could download your messages and transfer them to your new provider.

[Cupcakemumma]

okay thank you I might need to go to apple, cause I've had no success adding it to my Mac mail .