Is the neighbor entitled to demand the price of the signal booster (switch) he bought to connect the internet to his house after disconnecting from the shared network?

The questioner did not specify the reason for the dispute over the subscription fee. However, if the increase was from the company, the subscriber has no right to claim the switch. But if the increase was from your side: if it was fair, the subscriber bears the loss; and if it was unjust, then the subscription must be reduced, or the subscriber must be compensated for the value of the used switch at its current market price. If the dispute is due to you, then you must retract the cause or bear the cost of the switch. If it is due to him or the company, he has no right to claim it. An agreement can be reached to sell the switch, with each party bearing a portion of the loss, or to purchase it at a used price if you need it, or to refer the matter to specialists. The issue is simple and does not warrant further discord.