This code adds the "Add emoji" tool to the activity post form. This code uses elements of the "Ultimate Member - Private Messages", so this extension is required.

um_activity_post_insert_tools_emoji.php

<?php

// "Add emoji" tool for the activity post form.
add_action( 'wp_loaded', 'um_fix_emotize', 20 );
add_action( 'um_activity_post_insert_tools', 'um_activity_post_insert_tools_emoji' );

function um_activity_post_insert_tools_emoji() {
	if ( defined( 'um_messaging_plugin' ) ) {
		UM()->get_template( 'emoji.php', um_messaging_plugin, array(), true );
		wp_enqueue_script( 'um-messaging' );
		wp_enqueue_style( 'um-messaging' );
		add_action( 'wp_footer', 'um_activity_post_insert_tools_emoji_script', 20 );
	}
}

function um_activity_post_insert_tools_emoji_script() {
	?><script type="text/javascript">
		jQuery( function() {
			// Update caret position.
			jQuery( 'form.um-activity-publish' ).on('click touchend keyup', 'textarea.um-activity-textarea-elem', function(e) {
				e.target.umCaretPosition = um_getCaretPosition( e.target );
			});
			// Insert a smiley.
			jQuery( 'form.um-activity-publish' ).on('click', '.um-message-emolist span.um-message-insert-emo', function(e){
				e.preventDefault();
				e.stopPropagation();
				e.stopImmediatePropagation();

				var form = jQuery(e.delegateTarget);
				var code = jQuery(this).attr('data-emo');
				var chatbox = form.find('textarea.um-activity-textarea-elem');
				var old_pos = chatbox.prop('umCaretPosition') ? chatbox.prop('umCaretPosition').end : 0;

				var first_str = chatbox.val().substr( 0, old_pos );
				var last_str = chatbox.val().substr( old_pos, chatbox.val().length );
				var new_pos = ( first_str + ' ' + code + ' ' ).length;

				chatbox.val( first_str + ' ' + code + ' ' + last_str );
				um_setCaretPosition( chatbox.get(0), new_pos );
				chatbox.trigger('focus');
				um_Hide_Emobox();
			});
		} );
	</script>
	<style type="text/css">
		.um-activity-widget .um-message-emoji {
			float: left;
			position: relative;
		}
		.um-activity-widget .um-message-emoji .um-message-emo {
			color: #999;
			cursor: pointer !important;
			height: auto !important;
			line-height: 20px !important;
			min-width: 40px;
		}
	</style><?php
}

function um_fix_emotize() {
	if ( function_exists( 'UM' ) && isset( UM()->shortcodes()->emoji ) ) {
		$img = UM()->shortcodes()->emoji[':$'];
		unset( UM()->shortcodes()->emoji[':$'] );
		UM()->shortcodes()->emoji[':\$'] = $img;
	}
}