Student or Learner
Please let me know if strengthen is the right word in this context.
He is very weak in English. I have to strengthen his base.
You have come up with another interesting example. There is nor reason why you should not strengthen someone's base; I just don't think we do. Speaking purely personally, I would say either:
He (the learner) needs to work on/consolidate/improve his basic knowledge/basic skills/basics.
I (The teacher) need to work on/help him with/help him consolidate(?) his /basic knowledge/basic skills/basics.