There are a few plausible ways:
As someone mentioned in the comments; Alcohol works well for this. We have samples from a hundred years ago (e.g. Thylacine), which have been stored at room temperature in a museum for that period of time and have had DNA easily extracted from them.
Unfortunately for many species, alcohol preservation fell out of favour due to it shrinking (by dehydration) specimens, so that they no longer look "realistic" in terms of morphology (something that is very important for classical identification methods). In addition, ethanol and other alcohols tend to evaporate fairly fast if not sealed properly. For these reasons aldehyde based solutions came into favour about 100 years ago. The downside to this is that formaldehyde and other aldehydes cross-link the genetic material, making it more or less impossible to extract and use.
Another possible method is dehydration - mummification. Small samples like embryos or tissues can be dehydrated quite fast. In the absence of water, these samples should last more or less forever - we can extract DNA from mummies in many places around the world, but these ones might interest you in particular.
There are also specialist chemical solutions such as RNAlater that are routinely used in labs for preservation of precious genetic material.
Given that we knew these sorts of things in the 1980's and that the lab was staffed with competent scientists, and that they knew that the lab was going to shut down but would re-start at some time in the future, then it is entirely plausible that they would have used alcohol or something like RNAlater.
In the absence of this knowledge, but still competent scientists, it is much more likely that they would have used some sort of cold (frozen) storage method; whether this was cryopreservation (liquid nitrogen), such as is used for storage of cells or a specialist -80 $^\circ$C freezer or a -20 $^\circ$C freezer like you might find at your house. Some samples may have been still stored in chemical preservation in the interests of space-saving in freezers though.