Addition of -s at the end of verb

[aphyllum]

I have this present tense sentence where I'm unsure about the addition of -s for certain verb.

He fells down right after he gets the kite causing his leg to injure.

If you see from the sentence, how should I put the to injure? Since it is referring to leg which is singular, should I add -s? Or should it be in a past tense form since he gets the injury right after he gets the kite?

[Joe]

present
He falls down right after he gets the kite, causing his leg to be injured.
He falls down right after he gets the kite, causing injury to his leg.
He falls down right after he gets the kite, injuring his leg.

past
He fell down right after he got the kite, causing his leg to be injured.
He fell down right after he got the kite, causing injury to his leg.
He fell down right after he got the kite, injuring his leg.