From b2evolution manual

Look in _main.php (in the directory of your choosen skin) for

<?php $Item->Content(); ?>

this gives a result like:

=>Read more

Change it to

<?php $Item->content( '#', '#', 'Read More', '' ); ?>

for a result like this:

Read more

Change it to

<?php $Item->content( '#', '#', 'Read More', 'This is the rest of the post' ); ?>

for a result like this on the first page:

Read more

and this on the permalink page:

first part of post

This is the rest of the post

the rest of the post

Or change it to

<?php $Item->content('#','#',$Item->get('title'),'','<p>Read full text of ','...</p>','htmlbody',10); ?>

for a result like this:

Read full text of -this is the title of the post-

More technical info if you want to dig into it, you can find on http://doc.b2evolution.net/v-1-9/evocore/Item.html#methodcontent.

function content(
		$disppage = '#',
		$dispmore = '#',
		$more_link_text = '#',
		$more_anchor = '#',
		$before_more = '#',
		$after_more = '#',
		$format = 'htmlbody',
		$cut = 0,
		$stripteaser = false,
		$more_file = 
		)
@param mixed page number to display specific page, # for url parameter 
@param mixed true to display 'more' text, false not to display, # for url parameter 
@param string text to display as the more link 
@param string text to display as the more anchor (once the more link has been clicked) 
@param string string to display before more link/anchor 
@param string string to display after more link/anchor 
@param string Output format, see {@link format_to_output()} 
@param integer max number of words 
@param boolean true if you don't want to repeat teaser after more link was pressed 
@param string filename to use to display more