The list of files that you have you can create a dataset and then write that dataset to a CVS or a log (txt) file then email that to the end user within the body of the email.
Here is a sample of what I am referencing. you can copy and paste this into Task Builder
<AMFTP ACTIVITY="logon" SERVER="%var_FTPServer%" USERNAME="username" PASSWORD="AM5YgliO+fIhGgfn5GViDtz+qnX19JhV+4TCS9sxLtkI4k=aME" SESSION="FtpSession1" />
<AMFILESYSTEM ACTIVITY="write_file" FILE="%TaskVar_Log%">%now()% - INFO - Connection established</AMFILESYSTEM>
<!--Obtaining the file list-->
<AMFTP ACTIVITY="advanced" FTPCOMMAND="long_list" PARAMETER="*.*" FTPLONGLISTDATASET="ds_FileList" SESSION="FtpSession1" />
<AMFILESYSTEM ACTIVITY="write_file" FILE="%TaskVar_Log%">%now()% - INFO - List of files obtain. There are %ds_FileList.TotalRows% to be analyzed</AMFILESYSTEM>
This will need to be edited to work on your system with your FTP.