The only way I found to work was to use the VLC player (free) from
www.videolan.org Link for Windows
In the VLC media player, you can choose a drop down menu to "capture" the video more easily.
Steps:
1) If the video uses a Windows Media Player plugin, such as is seen in the original question, then you can right click on the video, choose properties, and you will see a URL to the .asx stream, for example:
http://www.lds.org/pa/multimedia/files/ ... 00k_wh.asx
2) Download the VLC player, go to the "media" menu, choose "Open a Network Stream", paste in the above URL, then use the drop-down option to choose "capture" (instead of play), near the bottom of that box.
3) Choose a destination file name ending with .asf and select the option for "Video- WMV + WMA (ASF)"
4) You can display the output if you want, but then click Start. That is it.
Regarding the other type of player, the kind seen at lds.org/move or at
http://www.lds.org/pa/display/0,17884,8776-1,00.html the previously mentioned method using the Firefox browser is best:
1) In firefox, after seeing the video, type in the address bar "about:cache" (without the quotes)
2) click on the link "list cache entries" in the section for Disk Cache Device
3) Search for "mp4" (or for lds.org) but eventually the complete URL ending in mp4 will be found, for example:
[url=http://about%3Cb%3E%3C/b%3E:cache-entry?client=HTTP&sb=1&key=http://broadcast.lds.org.att-idns.net/ReliefSociety/eng/RS_VT__03_BeckJB_Minister__eng__.mp4]
http://broadcast.lds.org.att-idns.net/R ... _eng__.mp4[/url]
If there is any difficulty, type this in the address bar: about:cache?device=disk
Then search for the mp4 link.
After you have that link, you can enter it directly in the browser (or click it). Then go to the File menu of the browser & select "save page as" to put it on your desktop.
If you need a file format converter,
SUPER is pretty good (the download link is at the bottom)