Well it's reasonable that if Quote ignores Booster, he'll stay alive longer maybe because of his obligation with Sue... He probably is able to fix the teleporter which sends him to the Sand Zone before dying...
Upon which maybe Jenka's dog finds Booster bringing him to Jenka which gives him a life pot, which repairs not only broken bones but glasses and robots! So, after a short meeting with Jenka, Booster heads back to Arthur's house in which he meets Quote. [When does me make the Booster upgrade? uhh... Maybe in his time at Jenka's house? or maybe before he goes to Arthur's house? Who knows...
[In best ending credits, Booster visits Jenka seemingly random! That's how I came up with this conclusion... Alternatively Booster already knew about Jenka or had met her in the past.. Who knows
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