When TM's get added or if they get added you should have one or two backpacks for TM's where you can only store TM's because I can just imagine how full your inventory is going to be if you can't store away your TM's. Maybe a vault with ALL shaded out TM's at the beginning when you've not collected any. And as soon as you do something like /tm 1 your tm vault opens up and you can shift click TM's in to the right slot. Example: I just got a Shadow Ball TM from a pokestop or however you'll get them. I do /tm 1 *Vault opens* Here I see all the TM's I can collect (sorted in type order, maybe first normal, then fire, water, electric etc.) and you can have different pages with all the TM's you can collect like in the pc but here you see all the TM's for each type. I will go to the right page for ghost and I will shift left click my shadow ball in and it will go to its right position in the tm vault. Something looking like this maybe: Spoiler: Example But with sorted TM's etc. I hope you understood what I mean and please let me know if you didn't and I'll try to explain it better. If this get added, don't make it something you have to pay for because everyone should have access to store away TM's.
Because TM's are not stackable as they each have different ID's your inventory is going to get filled up very quickly
To get a backpack would be great in general. Though it should be able to store not just Tms. It should also be able to store pokeballs and stuff.
