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The H5P plugin for WordPress received proper support for theming in version 1.17.4. However, 
H5P Group decided to keep the theme picker that allows you to set a global theme for all H5P content types 
an exclusive feature of H5P.com. This plugin fills that void and gives you the same options.
<h3>Install</h3>
Install from the WordPress plugin repository and activate.
<h3>Configure</h3>
You will find a new settings menu item labeled “H5P Themer”. It allows you to pick from a list 
of predefined themes or define your own custom theme. You can also choose the density, which 
influences how wide or compact H5P content will appear.

SNORDIAN's H5P Themer

Allows you to set themes for H5P content.

PLEASE NOTE: I gave some of my free time to create this plugin. Using it and its source code is absolutely free. I don’t want any money from you. However, if you like this plugin, I kindly ask you to make a one-time donation of 2.50 EUR to the Rainforest Coalition (https://www.rainforestcoalition.org/donate) — or more if you can afford to.
H5P is a versatile plugin to add interactive content to your website. You may try to run it inside some fields that are created by other plugins, e.g. inside tabs, accordions, lightboxes, etc. And with some of them it seems that H5P doesn’t work although it is, but the content is set to a height of 0 pixels. That problem is described at https://h5p.org/manipulating-h5p-with-javascript.
The best solution would be to modify the plugin that’s including tabs, etc. to your WordPress site, but that’s not always possible. In some cases, this plugin may be a feasible workaround at least.
In “observer” mode, it will try to add a so called ResizeObserver to the container that holds the iframe with H5P content. That observer will send a resize pulse whenever the container changes in size, e.g. when it becomes visible. This should be a safe option just taking some extra resources.
In “interval” mode, it will trigger H5P to resize in regular intervals which should let it be displayed in many cases. However, if they appear too frequent, they may cause the browser to stall. Choose the time interval wisely! Also, some H5P content types may break that way. The only way around this is then the “selector” mode.
In “selector” mode, you need to determine a CSS selector that will identify all the elements that you interact with to display other contents, e.g. the tab buttons. If that selector is set in the plugin’s settings, it will trigger a resize pulse when that element is clicked. This way, you prevent stalling the browser or breaking H5P content types. Depending on how the other plugin was created, there may not ba a suitable CSS selector then.
If necessary, you can use the manage_h5presizepulse_options capability to control access to the plugin settings.
PLEASE NOTE: H5P IS A REGISTERED TRADEMARK OF H5P GROUP. THIS PLUGIN WAS NEITHER CREATED BY H5P GROUP NOR IS IT ENDORSED BY THEM.

SNORDIAN's H5P Resize Pulse

Provides you with a potential workaround for H5P content that won't show in tabs, accordions, lightboxes, etc.

SNORDIAN's H5P Themer vs SNORDIAN's H5P Resize Pulse