Anyone know what ails this jasmine?

Posting on behalf of a friend, living in France, who says:

I came across this 'condition' on my jasmine plant this afternoon. The bottom pic shows the section that I touched with my finger. It is very milky. I thought first of the froghopper larva but this does not look like bubbled spit. What do you think? I'm not sure what to do about it!

Any ideas? Her sister-in-law suggested mealy bugs. I wondered if it could be some kind of fungus....

And here's a closeup of a bit she scraped off - looks almost like tapioca pudding!

 

First thought was woolly aphid, but depending on where your friend lives, it's a bit late in the season for that. The bottom pic definitely looks more like some sort of slime mould. If it's been very humid but mild there, that's the most likely culprit.
Unauthorized Access Despite the unfriendly-looking link, if you click and scroll down the page, there's something very similar. Mucilago crustacea or Dog Sick Slime Mould. Lovely!

 

Thanks @noisette47! She's in the Charente. I agree, it looks very like the euphoniously named "dog sick slime mould" in your link.

 

I was there last weekend, it was definitely persisting down

 

Slime mould is amazing stuff.

 

Probably one of the most interesting (but not the prettiest) life-forms on the planet , and not really related to anything else .
These remarkable organisms have the 'ability' to reconfigure their cellular structure according to the current conditions .
They normally exist as an amoeba-like single celled creature , but when the time is right to 'reproduce' (if that is the correct term) , they re-arrange themselves into a plant like structure , form a bulbous fruiting body , which then disperses the spores so the entire process can start again .
Thought someone on here may like to know that !