When you read this, does it feel the future "that will become" or the present "that has become"?
My grammar book goes for the latter, but I learned that to inifitive, though not necessarily, has a lot of future implications.
ex)She's the first woman to become President of the country.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
Once again, keannu, we tend to rely on common sense rather than worry about what someone once wrote about how certain constructions may, or may not, be used.