ı suppose there isn't a phone but there is telephone number because he/she says " you can call or you can send a short message" ,
if somebody says " telim var orada" we understand that my tel.number is there,you can use it.
no I think he speak with her (on internet or home phone) but he have to go so he tell her :
I have a (cell) phone where you can call or send a sms, I'm going out now