The uniqueness of each person’s microbiome means that some probiotics may take up residency in one person and not the other. If the probiotic comes from a fish or an algae, it is unlikely that a compatible support community of friendly bacteria will be found in a human. Below are studies finding that a probiotic took up residency in at least some people in a study. Residency is defined as being found 7 days after last administration. The studies must be on humans.
Enterogermina – Four Bacillus clausii Strains
- “Bacillus clausii was found alive in faeces for up to 12 days. In some volunteers, the recovered amount of OC, NR or SIN was higher than the number of administered spores.” 
- “Stool analysis showed that the probiotic E. coli had colonised all five persons for a period of 10 to 30 weeks (mean: 18.7 weeks, median: 25.7 weeks). In two individuals there was evidence of competition between host E. coli and probiotic E. coli, while in two others total E. coli levels increased persistently with at least a factor of 10 as a result of the received dose.” 
Probiotic preparation inVag(®) – women only
- “Molecular typing revealed the presence of Lactobacillus strains originating from inVag in 82% of women taking the drug at visit III (21 days), and 47.5% at visit IV. (28 days)” 
- “opical application of an ointment containing Lactobacillus gasseri LN40, L. fermentum LN99 and L. rhamnosus LN113…Topical application of a probiotic ointment is feasible to achieve persistence of lactobacilli for at least 10 days.” 
- Lactobacillus rhamnosus GG (Culturelle)
- “GG was also recovered in the faecal sample taken at the start of the intervention and at the time of the tissue sample collection, which indicates more persistent adherence of the probiotic” 
L. rhamnosus CNCM I-4036 (Human origin)
- “was identified after the intervention (t2) in fecal samples of volunteers that received this bacterial strain. This finding does not necessarily imply successful colonization but rather persistence of the strain at this time period. Detection of L. rhamnosus CNCM I-4036 for a much longer period would be needed to determine whether the strain does in fact colonize the gastrointestinal tract. 
- Lactobacillus rhamnosus (573L/1-3)
- ” The examined strains were detected in 37/46 (80.43%) patients after 5 days and in 19/46 (41.3%) patients after 14 days since the start of the treatment. L. rhamnosus 573L/1 strain colonised the G.I. tract more persistently.” 
- L. plantarum MF1298, DC13 (But not MF1291)
- ” MF1298 and DC13 persisted in the same volunteer after ended intake, suggesting host-specific persistence behaviour.” 
Does not Persist
- “Lactobacillus casei strain Shirota (Yakult) was undetectable with culture after 2 weeks of ceasing its consumption.” 
- “Streptococcal population was detected after 3 days of administration and persisted for 6 days after the treatment suspension.”  — did not make it to 7 days.
And the rest…
Assuming they do not take up residency is usually correct unless then are human sourced.