import * as (jasmine spyOn) not writable

I've had the same issue and the only workaround I found was to use babel-plugin-rewire.
I've created a very basic repo here if that can help.

Here are the main files:

• src/index.js

function bar() {
  return 42;
}

export function foo() {
  const result = bar();
  return result;
}

• test/index_test.js

import { foo, __RewireAPI__ as RewireAPI } from '../src/index';

describe('test foo', () => {
  it('should call bar', () => {
    const barSpy = jasmine.createSpy('bar');
    RewireAPI.__Rewire__('bar', barSpy);
    foo();
    expect(barSpy).toHaveBeenCalledWith();
  });
});

• karma.conf.js

module.exports = function (config) {
  config.set({

    // base path that will be used to resolve all patterns (eg. files, exclude)
    basePath: '',

    // frameworks to use
    // available frameworks: https://npmjs.org/browse/keyword/karma-adapter
    frameworks: ['jasmine'],

    // list of files / patterns to load in the browser
    files: ['test/index_test.js'],

    // list of files / patterns to exclude
    exclude: [],

    // preprocess matching files before serving them to the browser
    // available preprocessors: https://npmjs.org/browse/keyword/karma-preprocessor
    preprocessors: {
      'test/**/*.js': ['webpack', 'sourcemap'],
    },

    webpack: {
      mode: 'development',
      devtool: 'inline-source-map',
      module: {
        rules: [
          {
            test: /src\/.+\.js$/,
            use: {
              loader: 'babel-loader',
              options: {
                presets: ['@babel/preset-env'],
                plugins: ['rewire'],
              },
            },
          },
        ],
      },
    },

    // test results reporter to use
    // possible values: 'dots', 'progress'
    // available reporters: https://npmjs.org/browse/keyword/karma-reporter
    reporters: ['progress'],

    // web server port
    port: 9876,

    // enable / disable colors in the output (reporters and logs)
    colors: true,

    // level of logging
    // possible values: config.LOG_DISABLE || config.LOG_ERROR || config.LOG_WARN || config.LOG_INFO || config.LOG_DEBUG
    logLevel: config.LOG_INFO,

    // enable / disable watching file and executing tests whenever any file changes
    autoWatch: true,

    // start these browsers
    // available browser launchers: https://npmjs.org/browse/keyword/karma-launcher
    // browsers: ['Chrome'],
    browsers: ['MyHeadlessChrome'],

    customLaunchers: {
      MyHeadlessChrome: {
        base: 'ChromeHeadless',
        flags: ['--remote-debugging-port=9333'],
      },
    },

    // Continuous Integration mode
    // if true, Karma captures browsers, runs the tests and exits
    singleRun: false,

    // Concurrency level
    // how many browser should be started simultaneous
    concurrency: Infinity,
  });
};

• package.json

{
  "name": "webpack-karma-spy",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "scripts": {
    "test": "./node_modules/karma/bin/karma start"
  },
  "keywords": [],
  "author": "",
  "license": "ISC",
  "devDependencies": {
    "@babel/core": "^7.8.4",
    "@babel/preset-env": "^7.8.4",
    "babel-loader": "^8.0.6",
    "babel-plugin-rewire": "^1.2.0",
    "eslint": "^6.8.0",
    "eslint-config-airbnb-base": "^14.0.0",
    "eslint-plugin-import": "^2.20.1",
    "jasmine": "^3.5.0",
    "karma": "^4.4.1",
    "karma-chrome-launcher": "^3.1.0",
    "karma-jasmine": "^3.1.1",
    "karma-sourcemap-loader": "^0.3.7",
    "karma-webpack": "^4.0.2",
    "webpack": "^4.41.6"
  }
}

source: Can webpack 4 modules be configured as to allow Jasmine to spy on their members?

There's spyOnProperty which allows treating a property as read-only by setting the accessType argument to 'get'.

Your setup would then look like

import * as mod from 'my/module';
//...
const funcSpy = jasmine.createSpy('myFunc').and.returnValue('myMockReturnValue');
spyOnProperty(mod, 'myFunc', 'get').and.returnValue(funcSpy);