he carries a spare pair in his pocket just in case? Do all lubavitchers do that?
Rabbi Moshe Feller adopted the phrase, "never leave home without them". Many Lubavitchers carry a pair with them, the rest of us should be doing that. Even if you don't
always have a pair handy, if you are going to an event where you think you will meet people who haven't put on Tefillin, you will take a pair with you. This scene is relatively common, I've seen plenty of pictures of Eli Marcus, Benny, and others putting Tefillin on with musicians and sound tech guys at all kinds of music gigs.
The Rebbe taught us that we are all Shluchim. We each have the responsibility to impact everyone within our circle of influence. Here's a story about Avraham Fried doing that: ttps://www.youtube.com/watch?v=-7jKMQtUQx0