It is possible:
import scala.reflect.runtime.universe._
import scala.reflect.api
val mirror = runtimeMirror(getClass.getClassLoader) // whatever mirror you use to obtain the `Type`
def backward[T](tpe: Type): TypeTag[T] =
TypeTag(mirror, new api.TypeCreator {
def apply[U <: api.Universe with Singleton](m: api.Mirror[U]) =
if (m eq mirror) tpe.asInstanceOf[U # Type]
else throw new IllegalArgumentException(s"Type tag defined in $mirror cannot be migrated to other mirrors.")
})
assert(backward[String](forward[String]) == typeTag[String])