appropriate or not....

Well there are lots of factors you need to consider first before you can conclude that this is an evil scheme. How long have they been apart? Was the separation a messy one or did was it anonymous for both of them? If all the conditions are well when they parted ways then perhaps its just the ex making friends. But as you would expect that is rarely the case. You said the girl was a flirt right? I'm hoping that she is just a bit lonely and looking for someone to talk to. However, most often the ex tries to communicate with the current to mess the relationship that there currently is. Under good circumstances I don't think its not inappropriate for the ex to make contact with the present, but under the circumstance you gave me I'd be wary of this ex, maybe she is up to no good. Like you, most people won't even bother sending messages to their ex and that's why this is really suspicious. And I wonder how the ex got hold of the current's number too.

i think its not appropriate. the girl should not be doing that because it might cause misunderstanding with her boyfriend. just to protect the relationship from damage, i think she should not do it especially if she loves her BF.