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...He says that his Win 7 laptop actually "sees" his brother's wifi if he takes the laptop to that end of his house, but cannot actually connect to it....
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If a laptop's build-in wifi can see it, I bet a repeater would probably do it. It may not be the best way, but it would be a way with minimal fuss. Shop at a place where the repeater can be returned for refund. If it doesn't work, at least you are not stuck with a useless repeater.
Get the repeater with duo external antenna, one for IN and on for OUT; and get a power extension cord so the repeater is "mobile". If you don't have duct-tape, get a roll.
You can plug the repeater in, connect your laptop to it. Once laptop-repeater connection is established and you are in the repeater's management pages. You should be able to scan and see the available WiFi and signal strengths. Move the repeater around and find the best spot for his brother's WiFi (probably window facing the house with WiFi) and duct-tape the repeater there. The rest would be to follow the repeater's instructions and complete the setup selecting his brother's WiFi as the source to repeat. When you are comfortable the repeater works well at that spot, find ways to secure it there with something better than duct-tape.
If the signal is too weak to complete the set up, don't give up yet. Try one more thing. (The repeater I used, the user-guide actually suggested to do it this way first). Do the set up and initial testing where signal is strong, then move back to the space where you intend to use it, and find the best spot there. So, factory-reset the repeater (if it got started but failed to finish), go to his brother house to do the setup and verification, then go back home and plug the already-set-up repeater in. If it successfully reconnect, and reconnecting do seem to be less fussy than initial set up, now he can find the best spot for the repeater.
Good luck...