Tuesday's update to version 44 lets users opt in to receive notifications from websites even when a site's tab has been closed or never opened.
Google added the same functionality to Chrome in April with version 42.
Both Chrome and Firefox rely on the W3C's (Worldwide Web Consortium) under-construction "web push" protocol, and the associated Push API (application programming interface) for the feature.
Other changes in Firefox 44 include deprecation of support for the RC4 decipher over HTTPS connections safeguarded by TLS (Transport Layer Security), a move announced in September by all browser makers, who promised to drop RC4 support in 2016. The action was prompted by research that showed RC4 was easily cracked.
Google dropped RC4 with the update to Chrome 48 last week; Microsoft has said it will do the same for Internet Explorer (IE) and Edge at some point "in early 2016."
Firefox 44 also added support for the Google-created "Brotli" compression algorithm, which is up to 25% more efficient in squeezing files delivered to browsers, resulting in faster page loading times and reduced data consumption for those on capped connection plans.
More information about Firefox's push notifications can be found in this support document on Mozilla's website.
Firefox 44 can be downloaded for Windows (32- or 64-bit), OS X or Linux (32- or 64-bit.) Current Firefox users will automatically receive the upgrade.