以下是一个示例解决方法，展示了如何创建一个可复用的路由器变更观察者：

1. 创建一个名为RouterChangeObserverService的服务：

import { Injectable } from '@angular/core';
import { Router, NavigationEnd } from '@angular/router';
import { Observable, Subject } from 'rxjs';

@Injectable({
  providedIn: 'root'
})
export class RouterChangeObserverService {
  private routerChangeSubject: Subject;

  constructor(private router: Router) {
    this.routerChangeSubject = new Subject();
  }

  observeRouterChanges(): Observable {
    return this.routerChangeSubject.asObservable();
  }

  startObservingRouterChanges(): void {
    this.router.events.subscribe(event => {
      if (event instanceof NavigationEnd) {
        this.routerChangeSubject.next(event);
      }
    });
  }
}

2. 在需要使用路由器变更观察者的组件中，注入RouterChangeObserverService并使用observeRouterChanges()方法来订阅路由器变更事件：

import { Component, OnInit } from '@angular/core';
import { RouterChangeObserverService } from '路径/到/RouterChangeObserverService';

@Component({
  selector: 'app-my-component',
  templateUrl: './my-component.component.html',
  styleUrls: ['./my-component.component.css']
})
export class MyComponentComponent implements OnInit {
  constructor(private routerChangeObserver: RouterChangeObserverService) { }

  ngOnInit(): void {
    this.routerChangeObserver.observeRouterChanges().subscribe(event => {
      // 处理路由器变更事件
      console.log('路由器变更:', event);
    });
  }
}

3. 在需要触发路由器变更事件的地方，注入RouterChangeObserverService并调用startObservingRouterChanges()方法来开始监听路由器变更事件：

import { Component, OnInit } from '@angular/core';
import { RouterChangeObserverService } from '路径/到/RouterChangeObserverService';

@Component({
  selector: 'app-another-component',
  templateUrl: './another-component.component.html',
  styleUrls: ['./another-component.component.css']
})
export class AnotherComponentComponent implements OnInit {
  constructor(private routerChangeObserver: RouterChangeObserverService) { }

  ngOnInit(): void {
    // 触发路由器变更事件
    this.routerChangeObserver.startObservingRouterChanges();
  }
}

这样，MyComponentComponent组件就可以订阅并处理路由器变更事件，而AnotherComponentComponent组件可以触发路由器变更事件。