Hi, I am new here. My company has the old GLX Standard phones. Is there any way to transfer calls to a voicemail system?

Are you saying that you have a Voicemail system connected to the GLX? If you do have a Voicemail system, what brand is it? Im thinking that maybe you have a Voicemail box through your dialtone provider? More info needed.

Yes, I have a voicemail box through our dialtone provider. Is there a way to transfer calls to its mailbox or even better, to each extension in the mailbox?

Is there a way to transfer calls to its mailbox or even better, to each extension in the mailbox?
That would be a question for your mailbox provider. For example. When you dial your message center phone number, you probably dial a code then a password to log into your mailbox. There maybe a different code to dial that allows you to leave a message rather than retrieve messages. If this is true, then yes you can tranfer callers into a mailbox.