要在Angular中保存Stripe订阅的付款详细信息并创建订阅，可以使用Stripe的JavaScript客户端库和Angular的HttpClient库。下面是一个示例解决方案：

1. 安装Stripe和Angular的相关依赖：

npm install @stripe/stripe-js
npm install @angular/common/http

2. 在Angular项目的环境配置中添加Stripe的公钥：

// environments/environment.ts
export const environment = {
  production: false,
  stripePublicKey: 'your_stripe_public_key'
};

3. 创建一个StripeService来处理Stripe相关操作：

// stripe.service.ts
import { Injectable } from '@angular/core';
import { HttpClient } from '@angular/common/http';
import { environment } from 'src/environments/environment';

@Injectable({
  providedIn: 'root'
})
export class StripeService {
  private stripe: any;

  constructor(private http: HttpClient) {
    this.loadStripe();
  }

  private async loadStripe() {
    const stripe = await import('@stripe/stripe-js');
    this.stripe = await stripe.loadStripe(environment.stripePublicKey);
  }

  createSubscription(paymentMethodId: string): Promise {
    return this.http.post('/api/create-subscription', { paymentMethodId }).toPromise();
  }

  attachPaymentMethod(paymentMethodId: string): Promise {
    return this.http.post('/api/attach-payment-method', { paymentMethodId }).toPromise();
  }

  getStripe(): any {
    return this.stripe;
  }
}

4. 在组件中使用StripeService来创建订阅和保存付款详细信息：

// component.ts
import { Component } from '@angular/core';
import { StripeService } from './stripe.service';

@Component({
  selector: 'app-root',
  template: `
    Create Subscription
    Attach Payment Method
  `,
})
export class AppComponent {
  constructor(private stripeService: StripeService) {}

  async createSubscription() {
    const stripe = this.stripeService.getStripe();
    const { error, paymentMethod } = await stripe.createPaymentMethod({
      type: 'card',
      card: {
        number: '4242424242424242',
        exp_month: 12,
        exp_year: 2023,
        cvc: '123'
      }
    });

    if (error) {
      console.error(error);
      return;
    }

    try {
      const result = await this.stripeService.createSubscription(paymentMethod.id);
      console.log(result);
    } catch (error) {
      console.error(error);
    }
  }

  async attachPaymentMethod() {
    const stripe = this.stripeService.getStripe();
    const { error, paymentMethod } = await stripe.createPaymentMethod({
      type: 'card',
      card: {
        number: '4242424242424242',
        exp_month: 12,
        exp_year: 2023,
        cvc: '123'
      }
    });

    if (error) {
      console.error(error);
      return;
    }

    try {
      const result = await this.stripeService.attachPaymentMethod(paymentMethod.id);
      console.log(result);
    } catch (error) {
      console.error(error);
    }
  }
}

请确保替换your_stripe_public_key为您自己的Stripe公钥，并根据您的项目结构和后端API进行相应的调整。

这是一个基本的示例，您可以根据您的需求进行修改和扩展。