my friend says that if the mustache is connected to the beard its all called a beard but i think that's bull, confirm this?

There is no beard without a mustache. There are different names for facial hair under the lips ie.) goatee, soul patch, ect. Without the mustache growing in with the other facial hair it's not a beard

He is right, generically if a guy has a beard including a mustache then it is all called a "beard"--- you don't hear people distinguishing between the two whether it is connected or not, if it is a mostly full beard. I have had a beard for decades and including a mustache -- and always people have referred to it as a beard- not both.

You can have a beard WITHOUT a mustache,

but if you have both is usually just called a beard.

It's part of the beard but how does this really come up that it even needs to be discussed