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Thanks. So if I want to use 3phase availability here, I need to get them to install a wall charger?

Yes. The only way to get 3-phase into a Model 3 or Y is via a 3-phase wall charger.

Note that 3-phase only gives an extra 50% to the charge rate. It’s not 3x. That’s because the max the 3/Y on-board charger can do is 32A single phase (7.6 kW) or 16A 3-phase (11.5 kW).

For charging at work, I think even 7.6 kW is a lot more than you need. Charging at 15A or 3.6 kW gives about 22 km of range per hour, or 180 km over an 8 hour work day.
 
I have a MY rear wheel drive. Where I work, we have a 5 pin 32 amp 500V outlet on the wall next to my parking space. Can I use my mobile charger to charge my car while I'm at work (work is fine with it)? and is there a 5 pin adaptor that fits mobile charger? I think 3phase should not be used.
As long as it's actually 5 pin and not 4 pin - the charger requires a neutral connection.
 
Thanks. So if I want to use 3phase availability here, I need to get them to install a wall charger?
If your employer is up for it then why not?

If not, then maybe this portable 11kW charger might be suitable - it works the same as a fixed wall-charger and delivers 11kW of charging power, the maximum Tesla's can accept.
Being portable, on arrival at work when you're low on battery you would plug in, charge up during the day, and unplug and take it with you on your return journey home.
Note the charger linked above comes fitted with the Tesla charge-port button. Press it to stop charging and release the cable - saves you have to reach for the app or the fob.