Expires means only one thing, and this is not what you think:
The Expires entity-header field indicates the date / time after which the response is considered obsolete. [...]
The presence of the Expires field does not mean that the original resource will change or cease to exist earlier, before or after this time.
- RFC 2616 Β§14.21 , emphasis mine
If the URLs of Facebook images stop working after some point in time, this is their business. Their HTTP headers should not mention this, and in fact they do not.
However, I suspect that the URL parameter oe may contain an expiration timestamp. If I interpret 54be4ee2 as a hexadecimal number containing a UNIX timestamp, I get January 20, 2015, which is almost exactly a month later. Perhaps this is the value you are looking for?
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