How to pattern match with implicit conversion?

ClosestSolutionFound.scala

trait A {
  def toB: B
}
object A {
  def unapply(arg: A): B = arg.toB
}

sealed trait B {
  def isEmpty: Boolean = false
  def get: B           = this
}
case class B1() extends B
case class B2() extends B

object Main {

  val a: A = new A() {
    override def toB: B = B2()
  }

  val name: String = a match {
    case A(B1()) => "B1"
    case A(B2()) => "B2"
  }

  // or, of course:
  val name2: String = a.toB match {
    case B1() => "B1"
    case B2() => "B2"
  }
}

ImplicitConversionPatternMatching.scala

trait A {
  implicit def toB: B
}

sealed trait B
case class B1() extends B
case class B2() extends B

object Main {

  implicit class AOps(a: A) {
    implicit def toB: B = a.toB
  }

  val a: A = new A() {
    override implicit def toB: B = B2()
  }

  // How to make the following to compile without change?
  val name: String = a match {
    case B1() => "B1"
    case B2() => "B2"
  }
}